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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Uniform Continuity and Cauchy Sequences

  • Enzipino
  • · Replies 7 ·
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7

Graduate Name of a concept in math analysis in English

  • nuuskur
  • · Replies 2 ·
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2

Graduate What is measure of numbers with certain property on [0,1]

  • dimitri151
  • · Replies 4 ·
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4

Graduate Usefulness of partition of unity?

  • JonnyG
  • · Replies 8 ·
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8

Graduate What Is Mary Boas' Theorem III About Analytic Functions and Taylor Series?

  • DrPapper
  • · Replies 7 ·
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7

Graduate Extension of measure on sigma-algebra

  • Mike.B
  • · Replies 2 ·
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2

Graduate Prove gamma (n+1/2) = (2npi^1/2)/(n4^n) by induction

  • Pami
  • · Replies 1 ·
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1

Lemma on integrating forms over subvarieties with null preimages

  • HughBennet
  • · Replies 1 ·
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1

Graduate Unique Property of Convergent Series?

  • dimitri151
  • · Replies 3 ·
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3

Graduate Minimizing Aphi' + Bcos(phi) in [0,L] w/ phi(0)=0

  • dirk_mec1
  • · Replies 9 ·
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9

Graduate Multivariate piecewise fxn continuity and partial derivative

  • vchurchill
  • · Replies 1 ·
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1

Graduate How do metric scaling factors transform operators between coordinate systems?

  • Muthumanimaran
  • · Replies 1 ·
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1

When are two metrics equivalent?

  • wonguyen1995
  • · Replies 1 ·
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1

Graduate Piecewise Linear Programming with Multiple Functions

  • smehdi
  • · Replies 3 ·
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3

Graduate Does Poincaré conjecture require trivial higher homotopy groups?

  • jk22
  • · Replies 26 ·
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26

Showing a simple function is continuous on a restricted domain

  • kalish1
  • · Replies 1 ·
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1

Analysis of Implicit Differentiation

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Measurability of a function with finite codomain

  • hwangii
  • · Replies 2 ·
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2

Graduate Maxmimum\Minimum modulus principle

  • MMS
  • · Replies 3 ·
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3

Undergrad Expanding a Taylor series about a different point

  • MMS
  • · Replies 1 ·
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1

Construction of a Cauchy sequence

  • Paradox 101
  • · Replies 6 ·
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6

Graduate A sequence of functions evaluated at a sequence

  • AxiomOfChoice
  • · Replies 5 ·
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5

Graduate Intuition and visualization of cylinder sets in lattice systems

  • JorisL
  • · Replies 1 ·
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1

Graduate Why are separable spaces called "separable"?

  • pellman
  • · Replies 10 ·
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10

What is Stoll's definition of the natural logarithm function?

  • Math Amateur
  • · Replies 4 ·
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4

Continuity of inverse function at endpoints

  • Dave1
  • · Replies 1 ·
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1

Undergrad Why isn't the real part of z just the coefficient R?

  • whatisreality
  • · Replies 7 ·
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7

Graduate How to solve for a function that is asymptotic to a sequence

  • japplepie
  • · Replies 13 ·
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13

Complex function that satisfies Cauchy Riemann equations

  • beetlez
  • · Replies 2 ·
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2

Proof of Sum-Union Measure Inequality

  • mathmari
  • · Replies 1 ·
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1

Graduate Conditions on f for dx/f(x) to be a Measure in L^2

  • Jip
  • · Replies 4 ·
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4

Computing a Simple Integral Via Riemann Sums

  • Math Amateur
  • · Replies 4 ·
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4

Fundamental Theorem of the Calculus - Stoll: Theorem 6.3.2

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Every nonnegative real has an nth root proof

  • sonofagun
  • · Replies 9 ·
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9

Solving for $Mf \notin L^1(\mathbb{R})$ with $f \in L^1 (\mathbb{R})$

  • mathmari
  • · Replies 1 ·
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1

Riemann Criterion for Integrability - Stoll: Theorem 6.17

  • Math Amateur
  • · Replies 3 ·
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3

Showing the “only if” direction of equality in a complex equality

  • kalish1
  • · Replies 1 ·
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1

L'Hopital's Rule _ Statement of Theorem (Houshang H. Sohrab)

  • Math Amateur
  • · Replies 1 ·
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1

Proof of Darboux's Theorem (IVT for Derivatives)

  • Math Amateur
  • · Replies 7 ·
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7

Undergrad Numerical Approximation and addition of new data points

  • Geeniey
  • · Replies 11 ·
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11

Inverse Function Theorem for One Real Variable

  • Math Amateur
  • · Replies 2 ·
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2

Algebra of limits when individual limits don't exist

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Definitions of Lebesgue integral

  • DavideGenoa
  • · Replies 11 ·
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11

Graduate Rudin's Principles Theorem 1.11 (supremum, infimum)

  • ramleren
  • · Replies 3 ·
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3

Find the following in x + iy form

  • Logan Land
  • · Replies 2 ·
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2

Proof of Chain Rule for Differentiation - Stoll, Theorem 5.1.6

  • Math Amateur
  • · Replies 1 ·
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1

Trigonometric Inequality in Tom Apostol's Book

  • Math Amateur
  • · Replies 5 ·
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5

Can a finite set be compact?

  • Math Amateur
  • · Replies 7 ·
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7

Graduate What Are Imaginary Volumes in Complex Numbers and Algebras?

  • samsara15
  • · Replies 1 ·
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1

To Prove that The Level Set Of A Constant Rank Map is a Manifold

  • caffeinemachine
  • · Replies 3 ·
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3

Proving continuity of f* in Apostol Theorem 5.2

  • Math Amateur
  • · Replies 2 ·
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2

Metric Spaces - Fixed Point Theorem (Apostol, Theorem 4.48)

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Hypersurfaces of R^n are Orientable

  • WWGD
  • · Replies 5 ·
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5

Graduate Obstruction Theory and Embeddings

  • WWGD
  • · Replies 3 ·
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3

Graduate Prove f(z) = |z| is not analytic

  • inversquare
  • · Replies 16 ·
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16

Graduate Why does the double integral of (ds)² give (x−xᵢ)²/2 not (x−xᵢ)²?

  • member 428835
  • · Replies 14 ·
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14

Graduate Removable Singularity: Is it the Same as a Simple Pole?

  • MMS
  • · Replies 2 ·
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2

Graduate Real / Functional Analysis Video Lectures?

  • Knissp
  • · Replies 16 ·
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16

Why is infimum adherent to a set in Apostol's theorem 4.28?

  • Math Amateur
  • · Replies 3 ·
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3

Continuity and Compact Sets - Bolzano's Theorem

  • Math Amateur
  • · Replies 3 ·
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3

Graduate Is the Definition of Sigma Algebra Limited to Countable Unions?

  • AlonsoMcLaren
  • · Replies 1 ·
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1

Measure theory book covering Lebesgue measure and Hilbert spaces

  • mathmari
  • · Replies 1 ·
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1

Graduate Can a 4D shape exist in our universe?

  • Dean Whaley
  • · Replies 12 ·
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12

Graduate Why does x^n converge uniformly on [-α,α] but not on (-1,1)?

  • BrainHurts
  • · Replies 12 ·
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12

Challenge for Polynomial with Complex Coefficients

  • anemone
  • · Replies 1 ·
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1

Undergrad Definition of pointwise in mathematics?

  • Mr Davis 97
  • · Replies 4 ·
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4

Linear operator, its dual, proving surjectivity

  • Linux
  • · Replies 4 ·
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4

Apostal Chapter 4 - Cauchy Sequences - Example 1, Section 4.3, page 73

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Intersection of a closed convex set

  • Funky1981
  • · Replies 1 ·
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1

Graduate Physical explanation of e^i*pi=-1

  • THE HARLEQUIN
  • · Replies 4 ·
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4

Graduate Homogeneous but not additive function R→R

  • WWGD
  • · Replies 11 ·
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11

Every interval (a,b) contains both rational and irrational numbers

  • Math Amateur
  • · Replies 2 ·
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2

Does Cesaro-Stolz theorem apply when the limit is zero?

  • chisigma
  • · Replies 7 ·
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7

Graduate Proof that a TVS is seminormed iff it is locally convex

  • A_B
  • · Replies 2 ·
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2

Perfect Sets in R^k are uncountable - Issue/problem 2

  • Math Amateur
  • · Replies 5 ·
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5

Perfect Sets in R^k are uncountable

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Identifying the name of a theorem

  • nuuskur
  • · Replies 3 ·
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3

Graduate Existence of x,y so that x-y is in Z-{0}.

  • WWGD
  • · Replies 1 ·
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1

Heine-Borel Theorem - Proof - Rudin Theorem 2.41

  • Math Amateur
  • · Replies 5 ·
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5

Graduate Proof using the closed graph theorem

  • A_B
  • · Replies 2 ·
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2

Sequence of Intervals - Rudin, Theorem 2.38

  • Math Amateur
  • · Replies 1 ·
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1

Graduate Easy question regarding the basis for a topology

  • christian1357
  • · Replies 1 ·
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1

Complex Contour integration of rational function

  • Amad27
  • · Replies 24 ·
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24

Undergrad Is learning epsilon-delta proofs before analysis a good idea

  • Magenta55
  • · Replies 2 ·
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2

Graduate Real analysis exam problem on Lebesgue measure and density

  • Jaggis
  • · Replies 11 ·
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11

Graduate ArXiv:1301.7652 and Euler homogeneous function theorem

  • strangerep
  • · Replies 6 ·
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6

Graduate "Robustness" of Nielsen-Thurston Classification

  • WWGD
  • · Replies 1 ·
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1

Graduate Solving Equality Problem in Complex Numbers

  • kelvin490
  • · Replies 3 ·
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3

Graduate Explain this method for integrals (complex analysis)

  • Amad27
  • · Replies 4 ·
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4

Graduate Poincaré–Bendixson theorem behavior in planar dynamical systems

  • ShayanJ
  • · Replies 11 ·
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11

Evaluating a rational function with contour integration

  • Amad27
  • · Replies 1 ·
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1

Complex Contour Keyhole Integration Methods

  • Amad27
  • · Replies 5 ·
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5

Parametrizatrion of a Straight Line Segment in C - Simple Issue

  • Math Amateur
  • · Replies 2 ·
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2

Evaluating a logarithmic integral using complex analysis

  • Amad27
  • · Replies 5 ·
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5

Graduate Proving integral on small contour is equal to 0.

  • Amad27
  • · Replies 1 ·
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1

Graduate Proof of the Archimedean Property

  • Bashyboy
  • · Replies 9 ·
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9

Graduate Why are complex numbers central to analysis and physics?

  • Lapidus
  • · Replies 4 ·
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4

Graduate Covering space of implicit vs parametric functions

  • ellipsis
  • · Replies 6 ·
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6

Graduate Writing Elements in $L^p(X,Y,\mu)$ Mathematically

  • moh salem
  • · Replies 5 ·
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5

Can this inequality be proven under given conditions?

  • klim
  • · Replies 11 ·
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11