Topology and Analysis Forum

Participate in expert discussion on topology and analysis topics. This includes point-set topology, Real, complex, harmonic and functional analysis. Also measure and integration theory.

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Graduate Why spherical harmonics can only represent bounded functions on a sphere

  • pamparana
  • · Replies 1 ·
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1

Proving proposition 2.3.22 on absolute and conditional convergence in Sohrab

  • Math Amateur
  • · Replies 5 ·
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5

Graduate Can the Fejér Kernel Be Approximated by Polynomials?

  • Vannel
  • · Replies 1 ·
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1

Undergrad Necessity of absolute value in Cauchy Schwarz inequality

  • SamRoss
  • · Replies 4 ·
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4

Proving 1/n^p ≥ 1/n when p ≤ 1

  • Math Amateur
  • · Replies 4 ·
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4

Graduate How are topological spaces applied in the realm of physics?

  • Josh0768
  • · Replies 11 ·
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11

Proving 1/n! ≤ 1/(2·3^(n-2)) for n ≥ 3

  • Math Amateur
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2

Sohrab proposition 2.3.8: limit of r^n when |r| < 1

  • Math Amateur
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2

Undergrad Garling theorem 3.1.1: existence of least integers in supremum property

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad Garling Corollary 3.2.7: rational sequences converging to reals

  • Math Amateur
  • · Replies 7 ·
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7

What Are the Key Insights from D. J. H. Garling's Theorem 3.1.1?

  • Math Amateur
  • · Replies 6 ·
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6

Understanding Garling's Corollary 3.2.7 on Real Numbers and Rational Sequences

  • Math Amateur
  • · Replies 2 ·
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2

High School Precision Representation of Vectors Using a Spiral on a Sphere

  • metastable
  • · Replies 30 ·
2
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30

Why does Garling's definition of partial order omit reflexivity?

  • Math Amateur
  • · Replies 2 ·
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2

Deriving Lemma 1.2.11 from Lemma 1.2.4 via complements in Duistermaat and Kolk

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Proving Continuous Function: Expectation Values of Periodic Functions Over Time

  • thegaussian
  • · Replies 1 ·
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1

Uniform norm .... Garling Section 11.2 Normed Saces .... also Example 11.5.7

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Reproducing Kernel Hilbert Spaces

  • joshthekid
  • · Replies 3 ·
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3

Norm on bounded functions: proving homogeneity

  • Math Amateur
  • · Replies 2 ·
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2

Proving assertion (i) in Duistermaat and Kolk lemma 1.2.5

  • Math Amateur
  • · Replies 2 ·
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2

Bounded sets in normed spaces: Garling section 11.2

  • Math Amateur
  • · Replies 5 ·
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5

Necessary and Sufficient Meaning of Isometries by D. J. H. Garling

  • Math Amateur
  • · Replies 5 ·
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5

Undergrad Lemma 1.2.3 - Ethan.D.Bloch - The Real Numbers and Real Analysis

  • anhtudo
  • · Replies 2 ·
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2

Graduate What are the equality conditions for proving strict convexity?

  • member 428835
  • · Replies 1 ·
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1

Graduate Proving Ptolemy's inequality in Euclidean space R^n

  • ypatia
  • · Replies 1 ·
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1

Graduate Integrating |z|² dz along different paths from 0 to 1+2i

  • randybryan
  • · Replies 1 ·
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1

Span of orthonormal vectors in orthogonal complement (Garling 11.4.2)

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Trying to understand terms in a problem

  • Mr Davis 97
  • · Replies 6 ·
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6

Why does x_i equal the inner product in Garling's Gram-Schmidt remarks?

  • Math Amateur
  • · Replies 6 ·
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6

How Do We Know the Annihilator Operation Is Associative?

  • Math Amateur
  • · Replies 2 ·
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2

Proving A ⊆ A⊥⊥ in Garling's proposition 11.3.5-4

  • Math Amateur
  • · Replies 3 ·
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3

Reverse triangle inequality in Conway's example 5.3.4(b)

  • Math Amateur
  • · Replies 5 ·
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5

Cauchy-Schwarz inequality proof in Garling Proposition 11.3.1

  • Math Amateur
  • · Replies 2 ·
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2

Garling's Theorem 11.1.13 on pseudometrics and quotient spaces

  • Math Amateur
  • · Replies 5 ·
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5

Undergrad Bounded subsets and supremum of norms in Garling section 11.2

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Why does taking the supremum preserve inequality in the uniform metric?

  • Math Amateur
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2

Supremum of inequality in uniform metric triangle inequality proof

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Why do these functions form complete orthogonal systems in the Hilbert space?

  • member 428835
  • · Replies 19 ·
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19

Graduate Closures and Infinite Products

  • joeboo
  • · Replies 1 ·
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1

Graduate Has the 140-Year-Old Schwarz-Christoffel Math Problem Finally Been Solved?

  • Diffy
  • · Replies 1 ·
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1

Radius and Interval of Convergence for (x/sin(n))^n

  • Denis99
  • · Replies 3 ·
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3

Undergrad Running through a complex math derivation of plasma frequency

  • Suzanne Rosenzweig
  • · Replies 1 ·
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1

Undergrad Can someone explain these two examples of an open set

  • Austin Chang
  • · Replies 5 ·
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5

Undergrad Why Restrict Derivatives to Intervals?

  • member 587159
  • · Replies 25 ·
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25

Undergrad Parametrized set as plane through origin in McInerney 3.3.3

  • Math Amateur
  • · Replies 2 ·
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2

Integral Over Unit Sphere of Inner Product

  • joypav
  • · Replies 1 ·
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1

Graduate Ambiguity about roots of unity in discrete Fourier transform

  • CantorSet
  • · Replies 1 ·
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1

Graduate Arctan Identities Via Exponentiation

  • 4dhayman
  • · Replies 1 ·
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1

Undergrad Rank of Jacobian matrix in McInerney theorem 3.3.13

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Mechanical steps for the natural-neighbor interpolation

  • maistral
  • · Replies 1 ·
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1

Undergrad Pole Identification Using Block Diagram Reduction

  • Hraabo
  • · Replies 4 ·
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4

Undergrad Is the Unit Square Bijective or Only Injective to the Real Line?

  • nomadreid
  • · Replies 7 ·
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7

Graduate Schroeder's equation: simple observation

  • phoenixthoth
  • · Replies 1 ·
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1

Graduate Dirac delta function on the complex plane?

  • pellman
  • · Replies 1 ·
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1

Graduate How to test if a function has real or complex roots

  • Karlisbad
  • · Replies 1 ·
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1

Graduate What is the concept of the extended complex plane/Riemann Sphere?

  • jimmycricket
  • · Replies 1 ·
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1

Graduate Can the Gamma Function Simplify Complex Integrals?

  • Greg Bernhardt
  • · Replies 1 ·
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1

Graduate What are extended real numbers

  • Greg Bernhardt
  • · Replies 1 ·
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1

Insights What is a Real Number? A 5 Minute Introduction

  • Greg Bernhardt
  • · Replies 1 ·
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1

Graduate What is the Schwarz Inequality and Its Applications?

  • Greg Bernhardt
  • · Replies 1 ·
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1

Graduate Definition of Topology: What is a Topological Space?

  • Greg Bernhardt
  • · Replies 1 ·
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1

Finding Lebesgue Decomposition for a Measure Defined by an Integral

  • joypav
  • · Replies 3 ·
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3

Undergrad On the topological proof of the Fundamental Theorem of Algebra

  • swampwiz
  • · Replies 18 ·
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18

Graduate Why does the characteristic function not converge in the L1 space?

  • member 428835
  • · Replies 11 ·
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11

Differentiability of the product function in McInerney 3.1.5

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Finding all valid surfaces that go through a vector field

  • GabrielCoriiu
  • · Replies 9 ·
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9

McInerney Definition 3.1.1: linear approximation Ta(h)

  • Math Amateur
  • · Replies 2 ·
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2

Graduate What do the notations in functional analysis mean for a given function?

  • member 428835
  • · Replies 3 ·
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3

Undergrad Differential Forms.... Another question.... Browder, Sec 13.1

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Browder's definition of differential forms and Weintraub's example

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Wedge product determinant: Tu permutes rows, Walschap permutes columns

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Determinant formula with permutations in Walschap 1.3.1

  • Math Amateur
  • · Replies 6 ·
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6

Undergrad Anticommutativity of Wedge Product .... Tu, Proposition 3.21

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad The Wedge Product .... Tu, Section 3.7

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad Permutation for swapping tensor factors in Browder prop 12.25

  • Math Amateur
  • · Replies 6 ·
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6

Undergrad Applying Proposition 12.20 to alternating tensors in Browder 12.22

  • Math Amateur
  • · Replies 6 ·
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6

Undergrad Which branch of mathematics talks about this?

  • Swamp Thing
  • · Replies 13 ·
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13

Graduate Where is the actual space inside a tesseract?

  • empleat
  • · Replies 12 ·
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12

High School Finite distance between two points

  • CCMarie
  • · Replies 15 ·
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15

Undergrad Hausdorff dimension of Riemann zeta function assuming RH

  • nomadreid
  • · Replies 11 ·
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11

Vitali Covering: Proving Finite Interval Covering for m*(E)<∞

  • joypav
  • · Replies 1 ·
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1

"Approximation to the Identity" and "Convolution" Proof

  • joypav
  • · Replies 1 ·
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1

Browder Corollary 12.4: proving existence of nonzero covector

  • Math Amateur
  • · Replies 2 ·
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2

High School How can complex numbers be elevated to complex powers?

  • ForceBoy
  • · Replies 12 ·
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12

Is the basis in Tu's Proposition 3.1 general or the standard basis?

  • Math Amateur
  • · Replies 2 ·
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2

The Dual Space and Differential Forms .... ....

  • Math Amateur
  • · Replies 2 ·
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2

Rank one tensor coordinate transformation notation in Fortney

  • Math Amateur
  • · Replies 2 ·
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2

Reconciling definitions of 2-forms in Fortney, Darling and Weintraub

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Understanding why ##(y_n)_n## is a bounded sequence

  • JD_PM
  • · Replies 3 ·
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3

Undergrad Showing that a function is analytic

  • OscarAlexCunning
  • · Replies 2 ·
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2

Applying Banach fixed-point theorem to a nonlinear system in R²

  • mathmari
  • · Replies 9 ·
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9

Tangent plane equation from directional derivatives in Fortney

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Why does e^(2πi/3) equal both 1 and -1/2 + i√3/2?

  • Quarky nerd
  • · Replies 8 ·
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8

Approx. in $L^p$: Proving Existence of Subseq & $g$

  • joypav
  • · Replies 2 ·
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2

Proving Density of $S$ in $L^{p'}(E)$ for $g \in L^p(E)$

  • joypav
  • · Replies 1 ·
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1

Undergrad Error estimate for iterative convergence

  • member 428835
  • · Replies 5 ·
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5

Undergrad Do complex roots have a physical representation on a curve?

  • mohammed El-Kady
  • · Replies 6 ·
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6

Piecewise Continuous and piecewise smooth functions

  • comfortablynumb
  • · Replies 1 ·
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1

Undergrad How to think of S1 (circle) abstractly

  • vancouver_water
  • · Replies 18 ·
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18

Can we use a measure of rationals to count irrationals between them?

  • moyo
  • · Replies 12 ·
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12