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

How to Prove This Complex Inequality Involving Factorials and Sums?

  • klim
  • · Replies 1 ·
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1

Can This Complex Inequality Be Proven?

  • klim
  • · Replies 1 ·
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1

Graduate When to Use Modulus of Convexity and Modulus of Smoothness in Calculations?

  • moh salem
  • · Replies 1 ·
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1

Advanced Calculus - Differentiable and Converging Polynomials

  • bradyrsmith31
  • · Replies 2 ·
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2

Undergrad Why is the principal square root of a complex number not well-defined?

  • PFuser1232
  • · Replies 2 ·
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2

Graduate Reconstructing Group from Covering Maps

  • WWGD
  • · Replies 7 ·
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7

Graduate What Book Best Explains Fourier Transforms for Quantum Mechanics?

  • Avatrin
  • · Replies 1 ·
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1

Graduate Gaps In The System of Rational Numbers

  • Bashyboy
  • · Replies 29 ·
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29

Graduate Symplectic And Contact Manifolds

  • WWGD
  • · Replies 15 ·
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15

Every Cauchy sequence converges

  • evinda
  • · Replies 1 ·
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1

Graduate Are All Manifolds Defined to Be Hausdorff?

  • hideelo
  • · Replies 1 ·
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1

Graduate General Theorems on Bounding Manifolds?

  • WWGD
  • · Replies 1 ·
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1

Norm in R^d with Lebesgue measure

  • mathmari
  • · Replies 9 ·
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9

Is the Fourier Transform of an L1 Function Always Continuous and Bounded?

  • mathmari
  • · Replies 1 ·
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1

Show Inclusion of Measures: Hölder's Inequality

  • mathmari
  • · Replies 1 ·
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1

Show that it is metric and the measurable is 0

  • mathmari
  • · Replies 11 ·
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11
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6

Showing Connexity of $f(K)$ for Continuous $f$ on Connexe $K$

  • Julio1
  • · Replies 2 ·
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2

Assume the Limit Exists: Proving an Impossibility

  • Amad27
  • · Replies 5 ·
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5

Undergrad Functional Analysis vs. Complex Analysis?

  • Feynman's fan
  • · Replies 5 ·
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5

Is the Function Phi Lipschitz for Lebesgue Measurable Sets?

  • mathmari
  • · Replies 1 ·
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1

Graduate Is a Subset of the Eigenvector Matrix in PCA Equivalent to a Submanifold?

  • emmasaunders12
  • · Replies 15 ·
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15

Get a Detailed Proof of Stirling's Formula

  • Pratibha
  • · Replies 1 ·
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1

Graduate Question about Riemann Zeta Function

  • willr12
  • · Replies 2 ·
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2

Does Compactness Ensure a Positive Minimum for Continuous Functions?

  • kalvin
  • · Replies 1 ·
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1

Graduate What is the contradiction in the proof of Hahn Decomposition Theorem?

  • nateHI
  • · Replies 2 ·
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2

Considering the criterion for limit proofs

  • Amad27
  • · Replies 1 ·
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1

Graduate Is Notation Impacting Measurability in Tonelli/Fubini's Theorem?

  • nateHI
  • · Replies 3 ·
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3

Show that there is a continuous g with compact support

  • mathmari
  • · Replies 1 ·
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1

Prove Inequality: Nonnegative Reals {x}_{1}...{x}_{n} Sum to 1

  • Mathick
  • · Replies 1 ·
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1

What is the objective of proving the limit for max and min?

  • Amad27
  • · Replies 2 ·
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2

Graduate Continuity of an arc in the complex plane

  • Bashyboy
  • · Replies 4 ·
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4

Graduate Eigenvectors of Fourier transform operator #F:L^2\to L^2#

  • DavideGenoa
  • · Replies 1 ·
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1

Graduate Quotient space of the unit sphere

  • hedipaldi
  • · Replies 3 ·
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3

Graduate Harmonic Functions: Laplace's Equations & Analytic Functions

  • Fosheimdet
  • · Replies 3 ·
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3

Graduate Allowed values for the "differentiability limit" in complex analysis

  • V0ODO0CH1LD
  • · Replies 4 ·
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4

Graduate Analyticity of the complex logarithm on the negative real axis

  • Fosheimdet
  • · Replies 4 ·
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4

Proving ||u||_d = 0 and u=0 in Metric Spaces

  • Linux
  • · Replies 3 ·
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3

Laurent series, integral of a holomorphic function

  • Samwise1
  • · Replies 2 ·
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2

Analysis question involving Supremums and Infimums.

  • pineapplechem
  • · Replies 3 ·
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3

Can you check my proof for a limit formula

  • Amad27
  • · Replies 1 ·
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1
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2

How Does Subtracting a Limit Value Affect Convergence?

  • Amad27
  • · Replies 1 ·
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1

Concept of contour integration and integration along a square

  • Amad27
  • · Replies 27 ·
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27

Proof of the Irrationality of e - attributed to Joseph Fourier

  • Math Amateur
  • · Replies 2 ·
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2

Graduate More Complex Analysis studying recommendations

  • MelissaJL
  • · Replies 2 ·
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2

Graduate Identical Fourier coefficients of continuous ##f,\varphi\Rightarrow f=\varphi##

  • DavideGenoa
  • · Replies 2 ·
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2

What are the real and imaginary parts of z in terms of w?

  • yenyen
  • · Replies 1 ·
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1

Tough limit proof for a general f(x) and g(x)

  • Amad27
  • · Replies 5 ·
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5

Graduate Representing a function of one variable in terms of a sequence of gaussians

  • thoughtgaze
  • · Replies 2 ·
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2

Graduate Convergence Criteria for Box Topology on R^ω

  • hedipaldi
  • · Replies 2 ·
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2

Proving an Odd Function: ln(x+√(1+x²))

  • Yankel
  • · Replies 1 ·
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1

Undergrad What is the proof that the limit of a Cauchy sequence of integers is an integer?

  • xaara test
  • · Replies 3 ·
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3

Graduate Approximating simple function in $L_1$ with countable base

  • DavideGenoa
  • · Replies 1 ·
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1

Graduate Does (-2)^(⅔) have an imaginary component?

  • SafiBTA
  • · Replies 1 ·
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1

Graduate Special Properties of Hilbert Spaces?

  • WWGD
  • · Replies 33 ·
2
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33

Graduate Non-homeomorphis between CP^4 and CP^2 x CP^2

  • WWGD
  • · Replies 4 ·
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4

What Does Norm Convergence Mean in $L^p$ Spaces?

  • mathmari
  • · Replies 3 ·
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3

On integration, measurability, almost everywhere concept

  • kalish1
  • · Replies 1 ·
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1

Graduate Approximation of ##f\in L_p## with simple function ##f_n\in L_p##

  • DavideGenoa
  • · Replies 6 ·
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6

How Can We Generalize Lebesgue Measurable Functions in Higher Dimensions?

  • mathmari
  • · Replies 1 ·
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1

Graduate Complex analysis: residue integration question

  • Wheelwalker
  • · Replies 7 ·
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7

What is this theorem about measurable functions saying?

  • kalish1
  • · Replies 1 ·
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1

Why do the reals fill the rationals with the absolute value?

  • evinda
  • · Replies 2 ·
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2

Undergrad Every sequence has a convergent subsequence?

  • CoachBryan
  • · Replies 6 ·
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6

Graduate Definition of boundary, Stokes' theorem

  • tom.stoer
  • · Replies 6 ·
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6
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1

Graduate Why don't these open set axioms specify that the empty set is open?

  • dumb_curiosity
  • · Replies 13 ·
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13

Graduate Prove √a(n) Converges to 0 | Stuck on Proof

  • CoachBryan
  • · Replies 3 ·
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3

Lim of Convolution: Fourier Analysis Solution

  • Sonifa
  • · Replies 4 ·
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4

Is it enough to show that it is a Lebesgue measure?

  • mathmari
  • · Replies 1 ·
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1

Prove $\displaystyle \lim_{x \to 0}\frac{x}{1 + \sin^2(x)} = 0$

  • Amad27
  • · Replies 3 ·
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3

Graduate Fourier transform of function of a complex variable

  • thoughtgaze
  • · Replies 1 ·
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1

Graduate Lowest coefficient of the i part of Riemann exponents

  • David Carroll
  • · Replies 1 ·
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1

Graduate Abuse of notation in relative homology theory

  • andrewkirk
  • · Replies 7 ·
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7

Graduate Every bounded sequence is Cauchy?

  • CoachBryan
  • · Replies 2 ·
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2

Undergrad Is the Real Number Line Actually Infinite?

  • Stoney Pete
  • · Replies 2 ·
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2

Graduate Are Complex Analysis and Complex Variables the same thing?

  • Math10
  • · Replies 6 ·
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6

Undergrad Other names for the domain and range-straightening theorems?

  • quasar987
  • · Replies 2 ·
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2

Is Swapping Limits and Integrals Justified in Complex Analysis?

  • chisigma
  • · Replies 4 ·
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4

Cauchy Sequences: What it Means to be $|x_{n+1}-x_n|_p< \epsilon$

  • evinda
  • · Replies 11 ·
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11

Graduate Is F continuous if it is both upper and lower semicontinuous?

  • moh salem
  • · Replies 8 ·
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8

Graduate A misunderstanding of compact sets

  • scinoob
  • · Replies 12 ·
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12

Graduate Explaining Electroweak Theory Decomposition to a Beginner

  • noahcharris
  • · Replies 3 ·
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3

Graduate Measurability and Lebesgue integral of complex functions

  • DavideGenoa
  • · Replies 4 ·
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4

Proving an Infinite $\sigma-$Algebra is Uncountable

  • mathmari
  • · Replies 3 ·
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3

Find a subset of the real numbers

  • mathmari
  • · Replies 7 ·
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7

How to Calculate $\int_0 ^{\infty} \sin t^2$ Using Complex Analysis?

  • Jakob1
  • · Replies 21 ·
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21

Graduate Finding the Normal Cone of a Closed Convex Subset in a Hilbert Space

  • moh salem
  • · Replies 5 ·
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5

Why Is a Rectangle Considered Closed and Bounded in Volume Proofs?

  • mathmari
  • · Replies 1 ·
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1
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11

Graduate Two conditions of existence for Lebesgue integral

  • DavideGenoa
  • · Replies 2 ·
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2

The rectangle has an empty interior

  • mathmari
  • · Replies 15 ·
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15

Measure Union of n Measurable Sets: Formula & Examples

  • mathmari
  • · Replies 3 ·
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3

Show that the measure is equal to zero

  • mathmari
  • · Replies 5 ·
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5

Graduate Can I get some examples of a function with following properies

  • catsarebad
  • · Replies 14 ·
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14

Undergrad Why is preferable the line integral than the area integral over C plan

  • Jhenrique
  • · Replies 3 ·
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3

Graduate Conformal Mapping: Transforming Polygons to Circles?

  • JulieK
  • · Replies 5 ·
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5

Graduate Complex Analysis: Learning Resources and Practice Problems

  • MelissaJL
  • · Replies 5 ·
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5

Graduate Complements of Curves in Closed Surfaces: Homeomorphic?

  • WWGD
  • · Replies 3 ·
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3