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.

Sub-forums

Threads

Graduate How does the diameter of a closure relate to isolated points in Rudin's book?

  • Bachelier
  • · Replies 6 ·
Replies
6

Undergrad How Can I Express This Function with a Complex Square Root Term?

  • Big-Daddy
  • · Replies 7 ·
Replies
7

Graduate Understanding Sup of Sequence: S_n

  • Bachelier
  • · Replies 8 ·
Replies
8

Graduate Fundamental polygon of a Mobius strip

  • dumbQuestion
  • · Replies 6 ·
Replies
6

Graduate Logic Flawed? Is Rn Homotopic to Rm

  • dumbQuestion
  • · Replies 9 ·
Replies
9

Find $A_0$ in Root Mean Square & Parseval's Theorem

  • Dustinsfl
  • · Replies 3 ·
Replies
3

Understanding the Intriguing $\pi/2$ Integral Result

  • Dustinsfl
  • · Replies 5 ·
Replies
5

How Does the Triangle Inequality Apply to Complex Numbers?

  • Poirot1
  • · Replies 3 ·
Replies
3

Graduate Number of topologies on a 3-point set

  • middleCmusic
  • · Replies 8 ·
Replies
8

Graduate Papers by D. Carfi: extended spectral theory of distributions.

  • strangerep
  • · Replies 7 ·
Replies
7

Graduate Quotient Spaces and Homeomorphisms

  • snesnerd
  • · Replies 1 ·
Replies
1

Graduate When can we say a homotopy restricted to a subset is a homotopy itself

  • dumbQuestion
  • · Replies 2 ·
Replies
2

Graduate Analytic mapping from disk to disk must be rational

  • Grothard
  • · Replies 4 ·
Replies
4

Graduate Help understanding Laurent series in complex analysis

  • Waxbear
  • · Replies 8 ·
Replies
8

Graduate Is Every Point in a Subset of ℝ Either a Limit Point or an Isolated Point?

  • Bipolarity
  • · Replies 1 ·
Replies
1

Graduate Swapping Integrals and Sums: When is it Justifiable?

  • member 428835
  • · Replies 9 ·
Replies
9

Graduate Can Euler's Method Solve Higher Order Sums in the Basel Problem?

  • Parmenides
  • · Replies 2 ·
Replies
2

High School Is a Singleton a Connected Set?

  • Bachelier
  • · Replies 16 ·
Replies
16

How Does the Order of Convergence Relate to Numerical Schemes for ODEs?

  • MarkFL
  • · Replies 3 ·
Replies
3

What are the best definitions for limsup and liminf in sequences?

  • Poirot1
  • · Replies 1 ·
Replies
1

Graduate Curl and its relation to line integrals

  • member 428835
  • · Replies 3 ·
Replies
3

Graduate Exchanging derivative and improper integral

  • Galileo
  • · Replies 17 ·
Replies
17

Graduate How are Riemann surfaces graphed

  • saminator910
  • · Replies 1 ·
Replies
1

Graduate Is Bifurcation Topologically the Same?

  • rsaad
  • · Replies 2 ·
Replies
2

Graduate What happens with a differentiable function in the neighborhood of x?

  • Skalman
  • · Replies 5 ·
Replies
5

Confirm Answers on Homework Sheet: Subsequence Convergence

  • Carla1985
  • · Replies 3 ·
Replies
3

Converging Subsequences: Finding a Sequence for All Integers

  • Carla1985
  • · Replies 2 ·
Replies
2

Binomial Expansion Approximation for $\frac{1}{\sqrt{1 - A^2u^2}}$

  • Dustinsfl
  • · Replies 2 ·
Replies
2

Clovis's question at Yahoo Answers (bounded sequence)

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Graduate Conformal Mapping and flow normal to ellipse

  • nickthequick
  • · Replies 1 ·
Replies
1

Graduate Boundary of an open set in R2 is a limit point?

  • dumbQuestion
  • · Replies 5 ·
Replies
5

Graduate Quick question about Dirac delta functions

  • black_hole
  • · Replies 6 ·
Replies
6

Graduate Is a Circle Homeomorphic to a Subset of R^n?

  • joao_pimentel
  • · Replies 20 ·
Replies
20
Replies
3

Solve twice differentiable function

  • i_a_n
  • · Replies 1 ·
Replies
1

Infinite products defining entire functions

  • pantboio
  • · Replies 5 ·
Replies
5

Proving $f(x_k+εp)<f(x_k)$ with Taylor Series

  • i_a_n
  • · Replies 5 ·
Replies
5

Continuity in terms of closed sets

  • Fantini
  • · Replies 1 ·
Replies
1
Replies
3

Sequnce of rationals less than pi, which converges to pi

  • Amer
  • · Replies 10 ·
Replies
10

Graduate Is My Understanding of Vitali Sets Accurate?

  • Artusartos
  • · Replies 5 ·
Replies
5

Prove the limit of the nth root of n

  • Carla1985
  • · Replies 6 ·
Replies
6

Snell's Law and complex refractive indices

  • Nono713
  • · Replies 9 ·
Replies
9

Graduate Changing the orientation of a connected topological space

  • iLoveTopology
  • · Replies 3 ·
Replies
3

Graduate Taylor series expansion of Dirac delta

  • friend
  • · Replies 3 ·
Replies
3

Undergrad The Continutiy and the Convergence.

  • Tenshou
  • · Replies 13 ·
Replies
13

Graduate The illusory generality of metric spaces

  • h-simplex
  • · Replies 2 ·
Replies
2
Replies
5

Fresnel Integrals: Unsolved Question from MHF

  • Fernando Revilla
  • · Replies 3 ·
Replies
3

Graduate Measure of Reals: Countable or Uncountable?

  • cragar
  • · Replies 2 ·
Replies
2

Undergrad Why is the Euclidean norm crucial in vector analysis?

  • aaaa202
  • · Replies 4 ·
Replies
4

Graduate How would I prove that ln (lim (u)) = lim (ln (u))

  • MadViolinist
  • · Replies 4 ·
Replies
4

Graduate Proving Subdivision and Refinement: Is it as Simple as it Seems?

  • TheyCallMeMini
  • · Replies 5 ·
Replies
5

Graduate Is a Measure 0 Null Set Also Dense?

  • Bachelier
  • · Replies 4 ·
Replies
4

Graduate Could someone specify a metric on (0,1)

  • Bachelier
  • · Replies 1 ·
Replies
1

Residue at essential singularity

  • pantboio
  • · Replies 6 ·
Replies
6

Is the Function \( f(x,y) \) Continuous on \( \mathbb{R}^2 \)?

  • i_a_n
  • · Replies 3 ·
Replies
3

Confusion in proof involving lim and liminf

  • oblixps
  • · Replies 1 ·
Replies
1

Graduate Limit of integral lead to proof of convergence to dirac delta

  • lakmus
  • · Replies 4 ·
Replies
4

Graduate Analysis of vector fields, fourier and harmonics

  • SirAskalot
  • · Replies 2 ·
Replies
2

Graduate Questions about Attachments: Outer Measure and Infinity

  • Artusartos
  • · Replies 2 ·
Replies
2

Undergrad Proof of "If f(x) is Continuous, then |f(x)| is Continuous

  • macca1994
  • · Replies 13 ·
Replies
13

Compute Residues for Periodic Function with Multiple Poles?

  • pantboio
  • · Replies 5 ·
Replies
5

A proof question about continuity

  • i_a_n
  • · Replies 1 ·
Replies
1

.Proving Supremum of H: f(x)<d, [a,b]

  • solakis1
  • · Replies 7 ·
Replies
7

Graduate Where Did the 2's in the Denominator Go in the Fourier Analysis Proof?

  • Wingeer
  • · Replies 7 ·
Replies
7

Proof the convergence of a gamma sum

  • alyafey22
  • · Replies 5 ·
Replies
5

Graduate A question about Dirac delta function

  • James MC
  • · Replies 18 ·
Replies
18

Graduate Show that the preimage of dense set is dense?

  • mathgirl313
  • · Replies 2 ·
Replies
2

Undergrad A Closed set in the Complex Field

  • Bachelier
  • · Replies 5 ·
Replies
5

Proof about the continuity of a function of norm

  • i_a_n
  • · Replies 1 ·
Replies
1

Chen's question at Yahoo Answers (continuity of the norm).

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Graduate Inverse of Metric in Topology: Schwarz Inequality

  • Bachelier
  • · Replies 5 ·
Replies
5

Graduate Topology on Eculidean n-space(ℝ^n)

  • davechrist36
  • · Replies 5 ·
Replies
5

Undergrad How Do You Graph the Complex Function w = z^(i+2)?

  • alazhumizhu
  • · Replies 2 ·
Replies
2

Graduate What Constitutes something being coordinate free

  • saminator910
  • · Replies 9 ·
Replies
9

How Can I Solve This Integral Using Complex Integration?

  • pantboio
  • · Replies 11 ·
Replies
11

Graduate On continuous and locally one-to-one map

  • krete
  • · Replies 4 ·
Replies
4

Graduate Continuous functions on metric space, M

  • roman93
  • · Replies 3 ·
Replies
3

Graduate Can you think of quasi-norms which aren't norms?

  • danzibr
  • · Replies 2 ·
Replies
2

Graduate Is the Unit Interval [0,1] Open in Its Inherited Topology from the Real Line?

  • dapias09
  • · Replies 2 ·
Replies
2

The Geometry of Complex Numbers and the Confusion of $e^{i\pi} + 1 = 0$

  • I like Serena
  • · Replies 9 ·
Replies
9

Is a non-repeating and non-terminating decimal always an irrational?

  • reek
  • · Replies 2 ·
Replies
2

Graduate Dirac Delta Function: Does it Have a Residue?

  • elfmotat
  • · Replies 2 ·
Replies
2

Graduate Relationship between seminormed, normed, spaces and Kolmogrov top. spaces

  • Ocifer
  • · Replies 2 ·
Replies
2

Graduate Complex conjugate as a Mobius transformation

  • iLoveTopology
  • · Replies 3 ·
Replies
3

Graduate Contour integration of real functions

  • stefaneli
  • · Replies 4 ·
Replies
4

Graduate An Open and Closed Interval in Q

  • Bachelier
  • · Replies 14 ·
Replies
14

Undergrad Can We Assume Equality of Complex Numbers Based on Their Norm?

  • Bachelier
  • · Replies 6 ·
Replies
6
Replies
5

Why Is ln(1+x) Greater Than x/(2+x) for x > 0?

  • Lisa91
  • · Replies 1 ·
Replies
1

Graduate What Does the Third Axis Represent in Riemann Zeta Function Zeros Graphs?

  • SpaceDreamer
  • · Replies 1 ·
Replies
1

Graduate Dirac delta function how did they prove this?

  • galactic
  • · Replies 1 ·
Replies
1

A very interesting complex beta integral:

  • alyafey22
  • · Replies 5 ·
Replies
5

Integration a long closed curve is 0

  • alyafey22
  • · Replies 7 ·
Replies
7

Graduate Are open sets in R^n always homeomorphic to R^n?

  • iLoveTopology
  • · Replies 6 ·
Replies
6

Graduate How Does Length Extend to General Sets of Real Numbers?

  • Artusartos
  • · Replies 4 ·
Replies
4

Solve the following integral without complex analysis:

  • alyafey22
  • · Replies 9 ·
Replies
9

Graduate Countable intersection of F-sigma sets

  • jbunniii
  • · Replies 3 ·
Replies
3

Undergrad Natural Log : seems as a discontinous function

  • hms.tech
  • · Replies 4 ·
Replies
4