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 Ramanujan Summation and ways to sum ordinarily divergent series

  • bhobba
  • · Replies 41 ·
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Operator norm supremum inequality in Field's theorem 9.2.9

  • Math Amateur
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2

High School Introductory topology question after real analysis

  • Eclair_de_XII
  • · Replies 22 ·
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22

Operator norm: why sup and inf are actually max and min in Browder Lemma 8.4

  • Math Amateur
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2

Operator Norm for Linear Transformations: Browder Ch. 8, Section 8.1, Page 179

  • Math Amateur
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5

Operator norm definitions in Browder vs Field

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Embedding homeomorphic manifolds

  • Q-1
  • · Replies 42 ·
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42

The metrices are topologically but not strongly equivalent

  • mathmari
  • · Replies 10 ·
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10

The Elusive Field Structure of $\mathbb{R}^n$ Beyond $n=2$

  • Math Amateur
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3

How do I solve for a_3 in a complex Fourier series?

  • Tan Thom
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2
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4

Is the relation between limit points and closed sets clear? (Wondering)

  • mathmari
  • · Replies 8 ·
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8

Undergrad How Does Vector Subtraction Relate to Topology?

  • doggydan42
  • · Replies 19 ·
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19

Proving arcsin x is continuous on [-1, 1]

  • Math Amateur
  • · Replies 3 ·
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3
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2

Complex Square Root Function: Qs from Bruce P. Palka's Ex. 1.5, Ch. III

  • Math Amateur
  • · Replies 2 ·
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2

Where Does the Sign of n Matter in Palka's Examples?

  • Math Amateur
  • · Replies 2 ·
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2

How is Equation (1) Equivalent to the Derivative Definition in Theorem 7.1?

  • Math Amateur
  • · Replies 4 ·
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4

Graduate DFT k values and their dependence on interval length

  • SchroedingersLion
  • · Replies 4 ·
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4

Undergrad How to derive the Fourier transform of a comb function

  • arcTomato
  • · Replies 4 ·
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4

Undergrad Is a limit point compact subspace of a Hausdorff space necessarily closed?

  • facenian
  • · Replies 8 ·
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8

Undergrad Complex Fourier transform (represented by Σ)

  • arcTomato
  • · Replies 4 ·
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4

Undergrad How do charts on differentiable manifolds have derivatives without a metric?

  • jackferry
  • · Replies 20 ·
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20

Graduate Fourier transform and derivation

  • arcTomato
  • · Replies 7 ·
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7

Undergrad Differentiable manifolds over fields other than R, C

  • WWGD
  • · Replies 13 ·
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13

Verify Gamelin's Remark: Complex Square and Square Root Functions

  • Math Amateur
  • · Replies 3 ·
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3

Show that there is no order relation on K

  • mathmari
  • · Replies 9 ·
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9

Show that there exists a bijection

  • mathmari
  • · Replies 8 ·
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8
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2

Undergrad Discrete Topology and Closed Sets

  • joshthekid
  • · Replies 12 ·
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12

Undergrad What is wrong with this proof? (divergence of the harmonic series)

  • BWV
  • · Replies 6 ·
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6

Complex function with derivative only at zero

  • Math Amateur
  • · Replies 2 ·
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2

Proof of an Infimum Being Equal to the Negative Form of a Supremum ()

  • AutGuy98
  • · Replies 2 ·
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2

Undergrad Trouble with infinity and complex numbers

  • Troxx
  • · Replies 12 ·
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12

High School Why is equation (4.26) a quadratic form identity?

  • Heidi
  • · Replies 6 ·
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6

Understanding Differentiability and Continuity in Complex Analysis

  • Math Amateur
  • · Replies 2 ·
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2

Lim sup inequality in Denlinger theorem 2.9.6(b)

  • Math Amateur
  • · Replies 4 ·
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4

Denlinger theorem 2.9.6 (a): upper and lower limit inequality

  • Math Amateur
  • · Replies 2 ·
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2

Proof of upper and lower limits in Sohrab 2.2.39(a)

  • Math Amateur
  • · Replies 6 ·
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6

Undergrad Assigning a value for integrating a divergent oscillatory function to infinity

  • Swamp Thing
  • · Replies 8 ·
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8

Proving Sohrab's proposition 2.2.39 (b) on lim sup and lim inf

  • Math Amateur
  • · Replies 2 ·
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2

How Does Theorem 4.29 Illustrate Continuity Issues in Inverse Functions?

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Different metrics in different dimensions

  • Bob3141592
  • · Replies 2 ·
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2

Open covering in Apostol's Theorem 4.25 proof

  • Math Amateur
  • · Replies 2 ·
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2

Applying triangle inequality in Zill & Shanahan theorem 3.1.1

  • Math Amateur
  • · Replies 3 ·
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3

Convergence of coordinate sequences in R^n

  • Math Amateur
  • · Replies 6 ·
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6

Graduate How Does the Chain Rule Apply to Pushforwards in Differential Geometry?

  • sanad
  • · Replies 7 ·
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7

Carothers' Definitions: Neighborhoods, Open Sets, and Open Balls

  • Math Amateur
  • · Replies 2 ·
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2

Why does the discrete metric generate the power set topology?

  • Math Amateur
  • · Replies 2 ·
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2

Carothers exercise 32: open balls in normed vector spaces

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad Division of a complex number by zero

  • dyn
  • · Replies 7 ·
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7

Why closure points are characterized by open neighborhoods in Browder 6.8

  • Math Amateur
  • · Replies 3 ·
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3

Baire Category Theorem .... Stromberg, Theorem 3.55 .... ....

  • Math Amateur
  • · Replies 7 ·
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7

Graduate Baire Category Theorem proof in Stromberg 3.55

  • Math Amateur
  • · Replies 5 ·
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5

Why is bdry E empty iff E is both open and closed?

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Fourier Series = Re(Power Series)

  • joeblow
  • · Replies 3 ·
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3

Why is \( c'' \) an Upper Bound for \( U \cap [a, b] \) in Theorem 3.47?

  • Math Amateur
  • · Replies 2 ·
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2

Why does density of A in X let us select x ∈ A with ρ(x, z) < ε/2?

  • Math Amateur
  • · Replies 2 ·
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2

Graduate General formula for lenses without spherical abberation

  • mfb
  • · Replies 3 ·
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3
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5

Stromberg Lemma 3.44: why B_ε(x) ∩ A ⊃ B_{1/n}(x) ∩ A_{1/n}

  • Math Amateur
  • · Replies 2 ·
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2

Heine-Borel theorem: why does compactness imply boundedness in Stromberg 3.40

  • Math Amateur
  • · Replies 2 ·
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2

Proving U ⊂ S' in Stromberg's theorem 3.36

  • Math Amateur
  • · Replies 5 ·
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5

Proving a limit to infinity using epsilon-delta

  • brooklysuse
  • · Replies 3 ·
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3
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2

Why does Br(a) ⊂ Uj for all j when r = min{r1,...,rn}?

  • Math Amateur
  • · Replies 3 ·
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3

Finding Cluster Points/Accumulation Points

  • brooklysuse
  • · Replies 2 ·
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2

Why is the Series Absolutely Convergent for Sequences in l^2(N)?

  • Math Amateur
  • · Replies 2 ·
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Undergrad Theorem 4.3.4 in Sohrab: why f⁻¹(O') = S ∩ O

  • Math Amateur
  • · Replies 3 ·
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3

Heine-Borel Theorem .... Sohrab, Theorem 4.1.10 .... ....

  • Math Amateur
  • · Replies 2 ·
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2
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3

Undergrad Proving an open cover has no finite subcover in Sohrab 4.1.8

  • Math Amateur
  • · Replies 3 ·
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3

Why the open cover in Sohrab's Proposition 4.1.8 has no finite subcover

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Fractional Calculus and Residues

  • Harrisonized
  • · Replies 2 ·
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2

Sohrab Proposition 4.1.1: Lindelof property proof details

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad Compact Subsets of R .... Sohrab, Proposition 4.1.1 (Lindelof) ....

  • Math Amateur
  • · Replies 8 ·
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8

Graduate Functional differentiability: Frechet, but not Hadamard?

  • Testguy
  • · Replies 1 ·
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1

Graduate A question about the proof of the simple approximation lemma

  • Artusartos
  • · Replies 1 ·
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1

Lindelof covering theorem: countable subcover from uncountable set

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Lindelof covering theorem: countable subcollection from uncountable set

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Mapping of algebraic function to Riemann surface?

  • jackmell
  • · Replies 1 ·
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1

Graduate CW complex for infinite holed torus? (Surface of infinite genus)

  • dumbQuestion
  • · Replies 1 ·
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1

Graduate Topology: Munkres - Urysohn lemma

  • Fisicks
  • · Replies 1 ·
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1

Graduate Identifying Compact Sets in the Slitted and Moore Planes: What's the Method?

  • ForMyThunder
  • · Replies 1 ·
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1

Graduate Does SU(2) Commutativity Conflict with Its Non-Euclidean Structure?

  • Kontilera
  • · Replies 1 ·
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1

Graduate Is the Integral Inequality Possible to Prove for Certain Parameters?

  • amirmath
  • · Replies 1 ·
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1

Graduate Inquiry: Wavelet factorisation / Daubechies method /

  • MednataMiza
  • · Replies 1 ·
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1

Graduate Two definitions of locally compact

  • Fredrik
  • · Replies 1 ·
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1

Graduate How to Estimate the Operator Norm ||A||_2 for a Difference Operator?

  • Max Fleiss
  • · Replies 1 ·
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1

Sohrab Proposition 2.3.15 on e: inequality with lim inf

  • Math Amateur
  • · Replies 2 ·
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2

Sohrab Proposition 2.3.15: why does t_n ≤ s_n imply lim sup(t_n) ≤ e

  • Math Amateur
  • · Replies 4 ·
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4

Proposition 2.3.15: Understanding Sohrab's Basic Real Analysis Proof

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Sohrab Proposition 2.3.15: why does t_n ≤ s_n imply lim sup(t_n) ≤ e

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Proof of the L'Hôpital Rule for the Indeterminate Form

  • 3.1415926535
  • · Replies 2 ·
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2

Proving Sohrab Theorem 2.3.9(a) comparison test using Theorem 2.3.6

  • Math Amateur
  • · Replies 2 ·
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2

Graduate What does equilibrium mean in portfolio choice and asset pricing?

  • woundedtiger4
  • · Replies 1 ·
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1

Graduate The correct domain of self-adjointness for the Laplacian

  • AxiomOfChoice
  • · Replies 1 ·
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1

Graduate How to generalize Newtonian and Lagrangian mechanics

  • jostpuur
  • · Replies 1 ·
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1

Convergence of Sohrab Exercise 2.3.10 (1)

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Residue Proof of Fourier's Theorem Dirichlet Conditions

  • bolbteppa
  • · Replies 1 ·
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1