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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Threads

Uniform convergence - Length of graph

  • mathmari
  • · Replies 21 ·
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21

Convergence as for the cofinite topology on R

  • mathmari
  • · Replies 17 ·
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17

Undergrad Is [0,1] under the subspace topology Hausdorff, Compact, or Connected?

  • WWGD
  • · Replies 15 ·
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15

Graduate What Topological Vector Spaces have an uncountable Schauder basis?

  • lugita15
  • · Replies 6 ·
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6

Understanding Example from Topics in Banach Space Integration

  • Sara jj
  • · Replies 2 ·
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2

Solve Functional Equation on $\mathbb{Z}$

  • anemone
  • · Replies 1 ·
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1

Undergrad Jordan Measurement: Accuracy You Can Trust

  • graphking
  • · Replies 10 ·
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10

Undergrad Simplifying a nested radical that includes a complex number

  • cbarker1
  • · Replies 5 ·
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5

Graduate Can falling factorials be a Schauder basis for formal power series?

  • lugita15
  • · Replies 3 ·
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3

Laplace Convolution: f(t)=-5t^2+9

  • Alex2124
  • · Replies 2 ·
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2

Graduate How can visualizing abstract spaces aid in understanding mathematical concepts?

  • trees and plants
  • · Replies 29 ·
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29

Undergrad Basic measurement theory question

  • BWV
  • · Replies 5 ·
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5

Undergrad Skipping elementary calculus and starting at analysis?

  • Grasshopper
  • · Replies 12 ·
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12

Undergrad Analytic continuation of Dilogarithm

  • aheight
  • · Replies 7 ·
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7

High School Does uniform continuity of |f| imply uniform continuity of f?

  • Eclair_de_XII
  • · Replies 10 ·
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10

How can we prove the convergence of recursive defined sequences?

  • mathmari
  • · Replies 2 ·
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2

Real Number Pairs $(p,\,q)$ Satisfying Inequality

  • anemone
  • · Replies 2 ·
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2

Show that there is a 1-km section that he covers in 1.5 minutes

  • mathmari
  • · Replies 16 ·
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16

When is the Maximum Angle for Viewing a Tower from an Airplane?

  • mathmari
  • · Replies 12 ·
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12

Proving Differentiability of f at $x_0$

  • mathmari
  • · Replies 11 ·
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11

Trigonometric values for six angles on the unit circle

  • mathmari
  • · Replies 5 ·
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5

Undergrad What is the partition of unity used for in differential geometry?

  • Santiago24
  • · Replies 2 ·
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2

Undergrad Can we prove the correspondence between a real number with a point ?

  • fxdung
  • · Replies 7 ·
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7

High School Inequalities in the real numbers

  • mcastillo356
  • · Replies 18 ·
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18

Calculating derivatives for various functions

  • mathmari
  • · Replies 6 ·
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6

Value of f(1/2) using estimation for the remainder

  • mathmari
  • · Replies 14 ·
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14

Graduate Do Dynkin Diagrams Only Describe Lie Algebras?

  • phoenix95
  • · Replies 2 ·
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2

Do These Integrals Converge or Diverge?

  • mathmari
  • · Replies 29 ·
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29

Why does d ∈ D iff f(d-) < f(d+) in Browder 3.14?

  • Math Amateur
  • · Replies 2 ·
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2

Well-defined function that doesn't satisfy IVT

  • mathmari
  • · Replies 5 ·
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5

Woman and dog meeting distances while walking home

  • mathmari
  • · Replies 5 ·
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5

Composition of Two Continuous Functions .... Browder, Proposition 3.12 .... ....

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad A claim regarding Fourier Series

  • Raihan amin
  • · Replies 2 ·
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2

Undergrad Why +1 in Browder's Theorem 5.12 on Riemann integral existence

  • Math Amateur
  • · Replies 2 ·
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2

Why the +1 in Browder's Theorem 5.12 Riemann integral proof

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Compute Lebesgue integral as (improper) Riemann integral

  • SchroedingersLion
  • · Replies 5 ·
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5

Proving necessity in Browder's theorem 5.10 on Riemann integrals

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Curve of zeta(0.5 + i t) : "Dense" on complex plane?

  • Swamp Thing
  • · Replies 2 ·
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2

High School Question on a property of a function which is not a metric

  • trees and plants
  • · Replies 22 ·
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22

Undergrad Can Tensors of Any Rank Be Approximated by Matrices?

  • trees and plants
  • · Replies 26 ·
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26

Jacobian matrix of differentiable maps in Browder 8.21

  • Math Amateur
  • · Replies 2 ·
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2

High School Principal square root of a complex number, why is it unique?

  • mcastillo356
  • · Replies 13 ·
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13

Undergrad Is ##\delta##-steady needed in this proof, given ##\epsilon##-steady

  • yucheng
  • · Replies 2 ·
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2

Undergrad Any Good Lecture Series on Complex Analysis?

  • murshid_islam
  • · Replies 6 ·
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6

The Chain Rule in n Dimensions .... Browder Theorem 8.15 - Another Question ....

  • Math Amateur
  • · Replies 2 ·
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2

Cauchy sequence proof in Browder Proposition 8.7

  • Math Amateur
  • · Replies 2 ·
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2

Calculations with stepfunction(heaviside)

  • goohu
  • · Replies 2 ·
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2

Real Roots of Composite Polynomials: Solving P(Q(x))=0

  • anemone
  • · Replies 1 ·
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1

High School What is the Difference between imaginary part and imaginary number?

  • SHASHWAT PRATAP SING
  • · Replies 2 ·
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2

High School Applications of topological spaces not homeomorphic to R^n in physics

  • trees and plants
  • · Replies 14 ·
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14

Graduate Name for a subset of real space being nowhere a manifold with boundary

  • disregardthat
  • · Replies 5 ·
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5

Undergrad How Do Metric Space Properties Relate to Continuity?

  • trees and plants
  • · Replies 8 ·
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8

Graduate Integrability along a Hilbert space?

  • LieToMe
  • · Replies 16 ·
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16

Undergrad Can a U(1) Generator be Normalized to SU(1) through Determinant Condition?

  • DuckAmuck
  • · Replies 5 ·
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5

Mean value theorem in Cauchy-Riemann proof

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Is Fourier transformation an eigenproblem and unitary operator?

  • LagrangeEuler
  • · Replies 3 ·
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3

Undergrad Bijection between infinite and finite sets in real analysis proof

  • CaptainAmerica17
  • · Replies 29 ·
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29

Why is |1/√z| = 1/√|z| in Palka's complex analysis example?

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad A thought about the Riemann hypothesis

  • r731
  • · Replies 7 ·
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7

Graduate Is the Frechet Derivative of a Bounded Linear Operator Always the Same Operator?

  • LieToMe
  • · Replies 2 ·
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2

Undergrad About groups and continuous curves

  • LCSphysicist
  • · Replies 2 ·
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2

Graduate Applications of analysis in signal processing/machine learning?

  • Dowland
  • · Replies 5 ·
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5

Undergrad What are the applications of homology in understanding spaces and shapes?

  • trees and plants
  • · Replies 3 ·
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3

Question for Intermediate Analysis ()

  • AutGuy98
  • · Replies 2 ·
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2

Max Value of |bc| for Complex Numbers in Inequality

  • anemone
  • · Replies 2 ·
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2

Infinite dimentional subspace need not be closed

  • nwl
  • · Replies 2 ·
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2

Undergrad Why is [0,1] compact in the case of a collection of open neighborhoods?

  • Mathsadness
  • · Replies 9 ·
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9

Proof of the Equality of Supremums (Or Something Like That Anyway :) )

  • AutGuy98
  • · Replies 2 ·
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2

Supremum and infimum of B={(-1)^n+((-1)^n+1)/(2n)}

  • AutGuy98
  • · Replies 2 ·
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2

Solving a complex value equation

  • cbarker1
  • · Replies 4 ·
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4

Graduate Why is the standard basis in l2 space called a topological basis?

  • LagrangeEuler
  • · Replies 17 ·
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17

Pointwise and uniform convergence of n^α xe^(-nx)

  • mathmari
  • · Replies 11 ·
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11

When ratio test limit equals 1, what test should I use?

  • mathmari
  • · Replies 8 ·
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8

Using Cauchy Integral Formula for Laurent Series Coefficients

  • cbarker1
  • · Replies 2 ·
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2

Undergrad Differential analysis: convex functions

  • madafo3435
  • · Replies 2 ·
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2

Undergrad Partial fraction decomposition of Gamma function Euler form

  • benorin
  • · Replies 2 ·
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2

Undergrad Why Borel sets require closure under both unions and intersections

  • Math Amateur
  • · Replies 2 ·
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2

Why countable intersections and unions of open sets don't form Borel sets

  • Math Amateur
  • · Replies 2 ·
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2

Smallest σ-algebra containing countable sets in Axler example 2.28

  • Math Amateur
  • · Replies 5 ·
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5

Undergrad Why is this not a space-filling curve?

  • nomadreid
  • · Replies 12 ·
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12

Undergrad Smallest sigma-algebra containing countable or co-countable sets

  • Math Amateur
  • · Replies 5 ·
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5

Undergrad Courant and Fritz, Construction of the real numbers

  • GodfreyHW
  • · Replies 2 ·
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2

Undergrad Why does |x−x₀| not exceed |y−y₀|/5 in continuity proof?

  • GodfreyHW
  • · Replies 9 ·
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9

Undergrad Why Axler says the power set of ℝ is not a σ-algebra

  • Math Amateur
  • · Replies 3 ·
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3

Which property of σ-algebras does the power set of ℝ violate?

  • Math Amateur
  • · Replies 2 ·
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2

Graduate The map from a complex torus to the projective algebraic curve

  • victorvmotti
  • · Replies 27 ·
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27

Undergrad Why taking the infimum gives translation invariance in Axler 2.7

  • Math Amateur
  • · Replies 2 ·
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2

Translation invariance of outer measure in Axler 2.7

  • Math Amateur
  • · Replies 2 ·
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2

Finding Real Part of $z$ for Complex Numbers

  • anemone
  • · Replies 1 ·
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1

Undergrad Proving Lebesgue outer measure monotonicity from Carothers 16.2(i)

  • Math Amateur
  • · Replies 6 ·
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6

Proving the outer measure of an open interval equals b - a

  • Math Amateur
  • · Replies 7 ·
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7

Undergrad Expanding open sets and shrinking closed sets in Carothers Proposition 16.1

  • Math Amateur
  • · Replies 5 ·
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5

Expanding J_k and shrinking I_n in Carothers Proposition 16.1

  • Math Amateur
  • · Replies 2 ·
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2

Result 2.14 in Axler: outer measure of closed interval [a,b]

  • Math Amateur
  • · Replies 2 ·
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2

Proving outer measure inequality for closed intervals in Axler 2.14

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Proof of outer measure of a closed interval in Axler 2.14

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Can the Unit Interval be Measurably Split into Two Sets of Equal Length?

  • mathman
  • · Replies 6 ·
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6

Outer measure: proving |A| ≤ inf of coverings in Axler 2.5

  • Math Amateur
  • · Replies 4 ·
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4

Graduate How Can I Identify a Surface as a Cone in CAD Software?

  • tricha122
  • · Replies 2 ·
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2

Undergrad Alternative proof to a trivial problem

  • trees and plants
  • · Replies 43 ·
2
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43