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 Infinitely differentiable complex functions

  • ppy
  • · Replies 7 ·
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Graduate Dirac Delta Function: Explanation & Usage

  • dreamLord
  • · Replies 44 ·
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Undergrad Complex Power Operation: Is x^iy Possible?

  • scientificon
  • · Replies 3 ·
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Graduate Differentiating delta function composed with a function

  • rms502
  • · Replies 2 ·
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Graduate Interpreting ##\alpha \delta(x)##: Is ##\alpha## at ##x=0##?

  • matematikuvol
  • · Replies 1 ·
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Graduate How Can Abelian Integrals Be Simplified for Beginners?

  • bolbteppa
  • · Replies 6 ·
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6

Problem 15 section 5.1 from Bartle

  • bw0young0math
  • · Replies 6 ·
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6

Undergrad Proving Element In Union of Two Infinite Sets Not Necessarily In Intersection

  • woundedtiger4
  • · Replies 3 ·
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Graduate Does the Integral of a Derivative Equal the Function's Net Change?

  • jostpuur
  • · Replies 29 ·
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Undergrad What are upper and lower bounds and why are they important in mathematics?

  • woundedtiger4
  • · Replies 12 ·
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Graduate Proving a conjecture in complex analysis

  • Mandelbroth
  • · Replies 2 ·
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Graduate A good introductory book on real analysis with examples

  • bobby2k
  • · Replies 5 ·
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5

Graduate Measure theory question on integrals.

  • bolzano
  • · Replies 5 ·
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5

Compute Line Integral with Cauchy-Goursat Theorem

  • Fernando Revilla
  • · Replies 1 ·
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1

Compute Integrals: Integrate (z^3-6z^2+4)dz from -1+i to 1

  • asqw121
  • · Replies 3 ·
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3

Analytic Function I: Proving f(z)=log z Not Analytic on Domain D w/ γ

  • asqw121
  • · Replies 3 ·
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3

Analytic Function II: Complex Calculation

  • asqw121
  • · Replies 3 ·
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Graduate Bijections and need of zorn's lemma

  • jostpuur
  • · Replies 2 ·
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2

Solve Complex Logarithm Problem on Domain D | Yahoo! Answers

  • Fernando Revilla
  • · Replies 1 ·
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1

Graduate How Does the Lax-Milgram Theorem Utilize Continuity and Coercivity?

  • muzialis
  • · Replies 2 ·
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2

Nonstandard Analysis: Completeness of R via Every Limited Hyperreal

  • poissonspot
  • · Replies 3 ·
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3

High School Proof Writing for Dummies: Intersection & Union Elements

  • woundedtiger4
  • · Replies 3 ·
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3

Graduate Infinite Unions of Open/Closed Sets: Explained

  • aaaa202
  • · Replies 3 ·
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3

Complex Number Help: Find x+yi for z1,z1z2,z1/z2

  • Kris1
  • · Replies 12 ·
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12

Graduate Question about finite dimensional real l^p space

  • larkin1993
  • · Replies 2 ·
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2

Graduate On an intuitive level, density/countability of Q

  • johnqwertyful
  • · Replies 3 ·
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Graduate Q* (the set of rational cuts) has least upper bound property or not?

  • saurabhjain
  • · Replies 2 ·
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2

Graduate Contradictory (complex) integral transformation

  • ManDay
  • · Replies 12 ·
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12

Proving H is Complete & a Hilbert Space: Analysis of $\|.\|_H$

  • Impo
  • · Replies 5 ·
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5

Undergrad Proof about a limit property clarification

  • bonfire09
  • · Replies 4 ·
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4

Graduate Is f(x) a Contraction Mapping?

  • odck111
  • · Replies 3 ·
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Proving continuity with sequences

  • Carla1985
  • · Replies 7 ·
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7

Graduate Fourier Series/transform and eigenvalues

  • MrAlbot
  • · Replies 8 ·
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8

Proving Definition of Continuous Function: Hi, Carla!

  • Carla1985
  • · Replies 10 ·
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10

Undergrad Is (-1)^x a discontinuous function?

  • cp255
  • · Replies 3 ·
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3

Undergrad Natural examples of metrics that are not Translation invariant.

  • deluks917
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Graduate Can Dehn Twists Be Applied to Non-Orientable Manifolds Like the Moebius Strip?

  • tom.stoer
  • · Replies 4 ·
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Graduate The Cartesian product theorem for dimension 0

  • hedipaldi
  • · Replies 2 ·
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Graduate Laurent series - where does f(z) need to be holomorphic?

  • BruceW
  • · Replies 2 ·
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Graduate Proof of Continuity of $x^n$ from Pugh's "Real Mathematical Analysis" Chapter 1

  • Someone2841
  • · Replies 5 ·
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Graduate Calculating the density of optimally packed spheres

  • IridescentRain
  • · Replies 4 ·
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Graduate I proving something about my sequence

  • Jamin2112
  • · Replies 2 ·
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Graduate Are the Irrationals and Product Spaces Non-Homeomorphic?

  • hedipaldi
  • · Replies 8 ·
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8

Undergrad How to prove that Cosh(x) = Cos(ix)

  • cocopops12
  • · Replies 8 ·
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Graduate Functionals->functions of infinite variables?

  • HomogenousCow
  • · Replies 1 ·
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Graduate Quick Chebychev Inequality Question

  • Gooolati
  • · Replies 14 ·
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14

How Can You Prove Properties of Cells in Lattices Using the Complex Plane?

  • pantboio
  • · Replies 2 ·
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Graduate Real analysis epsilon delta problem

  • subsonicman
  • · Replies 1 ·
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1

Graduate Looking for Complex Analysis Video Course

  • antoan
  • · Replies 24 ·
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24

Undergrad Direct proof by using if then technique

  • woundedtiger4
  • · Replies 10 ·
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Graduate Real Analysis: Understanding Proof with Equations 3 & 4

  • woundedtiger4
  • · Replies 7 ·
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7

Graduate Topology problem about Hausdorff space and compactness

  • Jaggis
  • · Replies 20 ·
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20

Contraction mapping (Maryam Ishfaq's question at Yahoo Answers)

  • Fernando Revilla
  • · Replies 1 ·
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1

Graduate Can We Show Y=X If Y is a Subspace of X and Y^c is First Category?”

  • amirmath
  • · Replies 1 ·
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Graduate Is Every Continuous Function on an Unbounded Set Uniformly Continuous?

  • Bachelier
  • · Replies 8 ·
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8

Graduate Bilinear mappings, tensor products and p-summing operators

  • Trevor101
  • · Replies 4 ·
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4

Graduate Complex (contour indep.) integral of a branched integrand

  • ManDay
  • · Replies 4 ·
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4

Graduate Construct uncountably dense and holes everywhere

  • jostpuur
  • · Replies 8 ·
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8

Measurable Function (Another Question)

  • TheBigBadBen
  • · Replies 3 ·
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3

Measurable Function Composition: f∘g

  • TheBigBadBen
  • · Replies 3 ·
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3

Proving Null Sets: Lebesgue Measure and Lipschitz Functions

  • TheBigBadBen
  • · Replies 4 ·
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4

Graduate What is the Significance of Completely Regular Spaces?

  • friend
  • · Replies 125 ·
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Graduate Topology of punctured plane vs topology of circle?

  • nonequilibrium
  • · Replies 4 ·
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4

Graduate What Is the Hausdorff Dimension of \(\mathbb{Y}\)?

  • Bachelier
  • · Replies 2 ·
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Can improper integrals converge without absolute convergence?

  • alyafey22
  • · Replies 7 ·
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Graduate Equation of a line in complex plane

  • 4everphysics
  • · Replies 3 ·
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Graduate Confusion with Disconnected sets

  • Mr-T
  • · Replies 3 ·
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Can Gauss Curvature Be Zero on a Genus 2 Surface?

  • Poirot1
  • · Replies 1 ·
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Continuous Example: Weierstrass Function

  • Juliayaho
  • · Replies 2 ·
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Graduate Proving a sequence diverges directly

  • shoeburg
  • · Replies 2 ·
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2

Proving Lower Bound of $\int_{0}^{ \pi}\sin^{7}(x) \, dx$ is $(\pi/2)^7$

  • Juliayaho
  • · Replies 2 ·
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2

Graduate Scenarios where the Cauchy-Riemann equations aren't true?

  • thehangedman
  • · Replies 3 ·
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3
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2

Graduate Proving V is a Vector Space: Simplifying the Process with Axiom Lemma

  • Bachelier
  • · Replies 3 ·
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3

What is the imaginary part of the given function?

  • Poirot1
  • · Replies 2 ·
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2

Graduate Show L^p(E) is separable for any measurable E.

  • jpriori
  • · Replies 4 ·
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4

Troubling contradiction in Functional Analysis

  • ModusPonens
  • · Replies 1 ·
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1

Homeomorphism Between Q and Unit Sphere in R^3

  • Poirot1
  • · Replies 9 ·
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9

Graduate Simple notation question about subsequences

  • gottfried
  • · Replies 3 ·
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3

Graduate Rudin's explanation of how rapid the series 1/(n) converges

  • DeadOriginal
  • · Replies 3 ·
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3

Graduate Spectrum of a linear operator on a Banach space

  • AxiomOfChoice
  • · Replies 1 ·
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1

Dark Soul's question at Yahoo Answers (Laurent expansion)

  • Fernando Revilla
  • · Replies 4 ·
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4

Optimizing Least Square Method for Ill-Conditioned Linear Problems

  • Juliayaho
  • · Replies 8 ·
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8

Graduate How intuitive is the idea of completeness?

  • gottfried
  • · Replies 20 ·
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20

Graduate Proof: Complex entire function bounded by a monomial is a polynomial

  • Taedrin
  • · Replies 1 ·
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1

Borel and σ-algebra related question

  • Juliayaho
  • · Replies 1 ·
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1

Undergrad How to do circular curve fitting?

  • srinath1993
  • · Replies 2 ·
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2

Graduate Modulus of the difference of two complex numbers

  • Fourthkind
  • · Replies 5 ·
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5

Undergrad What Does F >= g Mean in a Function Definition?

  • jamesb1
  • · Replies 2 ·
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2

Graduate Understanding the Algebra of Branch Cuts in Multi-Valued Functions

  • sponsoredwalk
  • · Replies 3 ·
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3

Undergrad Can This Knot Be Identified from Knot Theory?

  • Mandelbroth
  • · Replies 1 ·
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1

Undergrad Log of i: Can you get logarithms of imaginary numbers?

  • theperthvan
  • · Replies 11 ·
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11

Graduate Can All Smooth Functions Near Zero Be Expressed by This Double Series?

  • Ben Niehoff
  • · Replies 1 ·
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1

Graduate Prove that the set of those $c$ is countable

  • zeraoulia
  • · Replies 2 ·
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2

Convert 7sqrt5 cis(tan−1 (2)) to Rectangular Form - Yahoo! Answers

  • MarkFL
  • · Replies 1 ·
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1

Graduate Seperable + What Implies Second Countable?

  • lugita15
  • · Replies 6 ·
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6

How is √2 μ Interpreted Geometrically?

  • Juliayaho
  • · Replies 3 ·
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3

What is the Result of Raising a Complex Number to a Power?

  • Petrus
  • · Replies 5 ·
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5

Graduate Help understanding equivalent definitions for continuity

  • TaliskerBA
  • · Replies 2 ·
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2