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

What is a function that is continuous at all points except the rationals?

  • Dustinsfl
  • · Replies 5 ·
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5

Continuous Except Jump Discontinuity: Showing True for Any Function

  • Dustinsfl
  • · Replies 1 ·
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1

Graduate Continuous function from (0,1) onto [0,1]?

  • dumbQuestion
  • · Replies 4 ·
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4

Graduate Complex analysis integration. Strange result

  • McLaren Rulez
  • · Replies 6 ·
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6

Graduate Proving monotonicity of a ratio of two sums

  • raphile
  • · Replies 3 ·
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3

Graduate What is e^-iPi/2 and how can it be represented using cos and sin notation?

  • DiracPool
  • · Replies 3 ·
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3

An interesting two variables function....

  • chisigma
  • · Replies 2 ·
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2

Undergrad Proofing the derivatives of e^x from the limit approach

  • ibelive
  • · Replies 19 ·
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19

Graduate Partial derivative exists at origin but not continuous there

  • mathFun
  • · Replies 4 ·
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4

Undergrad What is the meaning of that a function F is well-defiened ?

  • Maths Lover
  • · Replies 2 ·
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2

Undergrad How Does the Ratio Test Prove Series Convergence?

  • Bipolarity
  • · Replies 3 ·
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3

Graduate Conformal Mapping for Transforming Regions: Finding a Function

  • MaxJasper
  • · Replies 1 ·
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1
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2

Graduate What is [itex]{\delta ^n}(f(x))[/itex] in n dimensions?

  • friend
  • · Replies 15 ·
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15

Graduate What is the Set Intersection of Successive Midpoint Triangles in R^2?

  • rakehsoran
  • · Replies 3 ·
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3

Cantor Set Numbers: Explaining the Unique Ternary Expansion

  • Dustinsfl
  • · Replies 1 ·
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1

Graduate Complex analysis- show that the integral of this function exists

  • jrp131191
  • · Replies 3 ·
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3

Cantor ternary set, construction

  • Dustinsfl
  • · Replies 1 ·
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1
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1

Comparing the sup of two sequences

  • OhMyMarkov
  • · Replies 2 ·
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2

Graduate Finding inverse for a homeomorphism on the sphere (compactification)

  • huberscher
  • · Replies 13 ·
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13

Graduate Explanation of uniform topology theorem in Munkres

  • mathmonkey
  • · Replies 3 ·
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3

Graduate The circle as a set closed and bounded

  • dapias09
  • · Replies 7 ·
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7

Graduate Inverse of Function: Topology by Munkres Ch 1

  • trixitium
  • · Replies 2 ·
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2

Graduate What is Topological Equivalence in Functions and Dynamical Systems?

  • marellasunny
  • · Replies 3 ·
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3

Graduate Checking if a function is analytic or entire

  • fleazo
  • · Replies 1 ·
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1

Graduate Questions on locally compact space

  • jtceleron
  • · Replies 3 ·
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3

Graduate Can Direct Use of cosh(2y) and cos(2x) Prove the Trigonometric Identity?

  • MrWarlock616
  • · Replies 4 ·
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4

Undergrad Completeness axiom as having no holes in the set

  • Bipolarity
  • · Replies 4 ·
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4

Graduate Subspace topology of Rationals on Reals

  • dumbQuestion
  • · Replies 1 ·
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1

Undergrad Schwarz inequality is Cauchy–Schwarz inequality?

  • rfrederic
  • · Replies 5 ·
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5

Proving $\lim_{n\to\infty}a_n^2 = a^2$ with Delta-Epsilon

  • Dustinsfl
  • · Replies 4 ·
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4

Are All Countable Sets Closed?

  • OhMyMarkov
  • · Replies 5 ·
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5

Undergrad Taylor Series Interval of COnvergence and Differention + Integration of it

  • Square1
  • · Replies 2 ·
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2

Can we use the fact that $L>1$ to show that the sequence is unbounded?

  • OhMyMarkov
  • · Replies 11 ·
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11

Proof That $\lim\limits_{n\to\infty}\frac{1}{a^n}=0$ if $a>1$

  • Dustinsfl
  • · Replies 5 ·
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5

Progress and Accomplishments: A Look at What's Been Done

  • Uniman
  • · Replies 1 ·
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1

Graduate What is the value of the integral of a delta function over a finite interval?

  • benjamin_cro
  • · Replies 6 ·
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6

Dirichlet Problem on Sphere: Proving Mean Value of f

  • Dustinsfl
  • · Replies 1 ·
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1

Mean square convergence of Fourier series

  • Dustinsfl
  • · Replies 1 ·
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1

What Else Can the Poisson Kernel Achieve Beyond the Dirichlet Problem?

  • Dustinsfl
  • · Replies 1 ·
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1

The connection between integration and area

  • Poirot1
  • · Replies 3 ·
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3

Real Analysis is all about infinity

  • Tomp
  • · Replies 1 ·
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1

Graduate CR Equations: Real & Imaginary Parts Satisfy Cont. & Diff.

  • fleazo
  • · Replies 3 ·
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3

Graduate Is the Given Statement a Consequence of Fubini's Theorem?

  • Tatianaoo
  • · Replies 3 ·
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3

Undergrad Proof of Complex Number Formulas for Real & Imaginary Parts

  • CrazyNeutrino
  • · Replies 3 ·
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3

Undergrad Function Notation in Real Numbers: What Does it Mean?

  • HasuChObe
  • · Replies 3 ·
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3

Graduate How Does the Riemann Integral Affect Lp Space Completeness?

  • dumbQuestion
  • · Replies 3 ·
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3

Continuous periodic piecewise differentiable

  • Dustinsfl
  • · Replies 1 ·
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1

Understanding theorem in Fourier series

  • Dustinsfl
  • · Replies 1 ·
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1

Graduate Lebesgue outer measure of a set of countably many points is 0 - logic check

  • dumbQuestion
  • · Replies 9 ·
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9

Graduate Open subset of R written as a countable union of pairwise disjoint open intervals?

  • dumbQuestion
  • · Replies 3 ·
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3

Proving Schwarz's & Triangle Inequalities for Infinite Sequences

  • Dustinsfl
  • · Replies 1 ·
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1

Limit Points of Unbounded Interval

  • OhMyMarkov
  • · Replies 1 ·
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1

Graduate Epsilon proof and recursive sequences

  • dustbin
  • · Replies 4 ·
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4

How can I prove that the infinite union of certain closed sets is not closed?

  • OhMyMarkov
  • · Replies 3 ·
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3

Graduate Why Is \left[\frac{1}{2},1\right] a Neighborhood of 1 in \left[0,1\right]?

  • funcalys
  • · Replies 5 ·
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5

Prove Schwarz's & Triangle Ineqs for Inf Seqs: Abs Conv

  • Dustinsfl
  • · Replies 8 ·
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8

Solving Abs Converge Issue with Ratio Test

  • Dustinsfl
  • · Replies 1 ·
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1

The minimal uncountable well-ordered set

  • topsquark
  • · Replies 1 ·
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1

Bounded Set with Two Limit Points

  • OhMyMarkov
  • · Replies 3 ·
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3

Graduate Compactness/convergence in Banach spaces

  • TaPaKaH
  • · Replies 5 ·
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5

Laplace general soln (x-x_0)^2 + (y-y_0)^2\leq R^2

  • Dustinsfl
  • · Replies 1 ·
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1

Undergrad Undergraduate courses for the study of fractals

  • Mathematicize
  • · Replies 1 ·
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1

Calculation in proof of Poincare's Lemma

  • oblixps
  • · Replies 4 ·
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4

Graduate Question on constructing a convergent sequence

  • ScroogeMcDuck
  • · Replies 1 ·
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1

Graduate Does the Gaussian have complex poles?

  • mjordan2nd
  • · Replies 2 ·
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2

Graduate Proof of "Every Cauchy Sequence is Bounded

  • fderingoz
  • · Replies 3 ·
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3

Graduate Uniform Convergence: Intuitive Explanation

  • stephenkeiths
  • · Replies 2 ·
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2

What is the correct formulation of the problem: $0^{0}$?

  • chisigma
  • · Replies 3 ·
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3

Graduate Variation of Dirac delta function

  • friend
  • · Replies 5 ·
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5

Graduate Functional analysis - question about separable dual spaces

  • AxiomOfChoice
  • · Replies 10 ·
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10

Graduate Closed or open question about the Extended Real line

  • Fractal20
  • · Replies 4 ·
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4

Graduate Complex Analysis Solutions: Real and Imaginary Parts

  • Fabio010
  • · Replies 1 ·
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1

Is the Sequence $\{x_n\}$ Defined by $7x_{n+1} = x_n^3 + 6$ Increasing?

  • Dustinsfl
  • · Replies 3 ·
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3

Graduate How Can I Better Understand Advanced Calculus Proofs?

  • NukeEng101
  • · Replies 3 ·
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3

Graduate What is the Definition of Closed Sets in Topology?

  • kimkibun
  • · Replies 4 ·
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4

Graduate Proving Openness of a Set in n-Dimensional Space | Math Proof

  • stauros
  • · Replies 2 ·
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2

What is the Limit of the Poisson Kernel Prove for $r\to 1$?

  • Dustinsfl
  • · Replies 10 ·
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10

Proving Steady State Temperature Distribution in a Disk

  • Dustinsfl
  • · Replies 1 ·
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1

Prove Evenness of Poisson Kernel for Fixed $r$

  • Dustinsfl
  • · Replies 1 ·
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1

Proof of Positive Values for P(r,θ)

  • Dustinsfl
  • · Replies 1 ·
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1

Graduate Quotient Topology and Adjunction Space

  • sammycaps
  • · Replies 5 ·
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5

High School Definition Of The Complement Of A Set

  • Bashyboy
  • · Replies 2 ·
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2
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2

Undergrad Analytic Continuation of the Exponential Function

  • spaderdabomb
  • · Replies 17 ·
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17

Fn converges Uniformly to f, prove that f is continuous

  • Amer
  • · Replies 7 ·
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7

Is Poisson's Kernel Useful for Computing Sums of Cosine Functions?

  • Dustinsfl
  • · Replies 2 ·
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2

Graduate Extract Real Part From ln(e^{ix}+i)

  • cragar
  • · Replies 4 ·
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4

Squared Difference of Two Series: Why?

  • Dustinsfl
  • · Replies 3 ·
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3
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4

Undergrad Decompose Even & Odd parts of a function?

  • radiator
  • · Replies 6 ·
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6

Graduate Can anybody help me to understand this proof?

  • Artusartos
  • · Replies 8 ·
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8

Graduate Clarifications on the least upper bound property and the irrational numbers

  • drobadur
  • · Replies 3 ·
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3

Graduate Contour Integration with Singularities: How Does the Residue Theorem Apply?

  • chill_factor
  • · Replies 2 ·
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2

Graduate [Help]Cauchy-Riemann Equations Proof

  • kostas230
  • · Replies 5 ·
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5

Graduate Regarding Einstein Summation Convention

  • clayton26
  • · Replies 2 ·
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2

Graduate How to compute inner product in the Hardy space

  • LikeMath
  • · Replies 1 ·
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1

Graduate Question about supremum and infimum

  • hkcool
  • · Replies 2 ·
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2

Greatest integer function with linear function inside

  • Amer
  • · Replies 2 ·
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2