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 Problem on integrating dirac delta function

  • tan90ds
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Graduate Constructing a premeasure on half open intervals

  • c4rpe
  • · Replies 2 ·
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Undergrad I don't understand uniform continuity

  • Arian.D
  • · Replies 42 ·
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Graduate How Is the Residue Calculated for 1/(z^2+4)^2 at z=2i?

  • bugatti79
  • · Replies 4 ·
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4

Graduate Does Fourier series of x^2 converge?

  • gauss mouse
  • · Replies 6 ·
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6

Proof: Let $f$ be a Nonconstant Entire Function on the Unit Disc

  • Dustinsfl
  • · Replies 7 ·
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7

Graduate Understanding Measure Theory: Countably Additive Functions and σ-Algebras

  • woundedtiger4
  • · Replies 7 ·
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7

How to Calculate the Residue of \(\frac{\sin z}{z^n}\)?

  • Dustinsfl
  • · Replies 3 ·
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3

All complex # satisfying the equation

  • Dustinsfl
  • · Replies 3 ·
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3

Undergrad What really are intervals in respect to functions ? As defined they

  • Kartik.
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2

Graduate Regions of the complex plane - finding the locus

  • autodidude
  • · Replies 16 ·
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16

Graduate Is this a valid argument about box topology?

  • Pippi
  • · Replies 5 ·
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5

Why Does a Meromorphic Function Have Only Countably Many Zeros?

  • Dustinsfl
  • · Replies 1 ·
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Verifying CR Equations for $z\cos z$

  • Dustinsfl
  • · Replies 3 ·
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3

Proving Meromorphic Function Equality w/ Liouville's Theorem

  • Dustinsfl
  • · Replies 1 ·
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Finding the Zeros of $1+z^{2^n}$ on the Unit Disc

  • Dustinsfl
  • · Replies 3 ·
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3

Partial Sum Bounds: Explaining the Shift from N to $2^{N+1}-1$

  • Dustinsfl
  • · Replies 4 ·
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4

Graduate Continously differentiable f: R^n -> R^m not 1-1?

  • ryou00730
  • · Replies 10 ·
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10

Undergrad Do Alternating Series Have Limits?

  • I'm Awesome
  • · Replies 12 ·
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12

Graduate Limit proof on monotonic sequences

  • Bipolarity
  • · Replies 11 ·
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11

Graduate Bilinear Function: |B(h,k)| / |(h,k)| = 0 for Lim (h,k) -> (0,0)

  • brydustin
  • · Replies 2 ·
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2

Undergrad Differentiability of composite functions

  • raphile
  • · Replies 3 ·
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3

Graduate How to Prove ℝn is Not Homeomorphic to ℝm for m≠n?

  • 6.28318531
  • · Replies 11 ·
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11

Undergrad Uncovering the Truth about e: Proofs and Derivatives

  • dextercioby
  • · Replies 4 ·
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4

Graduate Hausdorff Space and finite complement topology

  • Pippi
  • · Replies 2 ·
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2

Graduate What is the Definition of Compactification for a Topological Space?

  • Flying_Goat
  • · Replies 2 ·
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2

Graduate Is it true that anything coarser than the cofinite topology is not T1 and

  • GridironCPJ
  • · Replies 1 ·
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Graduate What does it mean when math text authors use the word pathological ?

  • gakushya
  • · Replies 2 ·
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Graduate Proof for Angle Preserving Transformation: Eigenvalues Same Magnitude

  • brydustin
  • · Replies 1 ·
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Graduate What is the most efficient method for computing exp(tA)?

  • brydustin
  • · Replies 14 ·
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14

Converges to a holomorphic function on D(0,1)

  • Dustinsfl
  • · Replies 8 ·
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8

Show convergence of weierstrass product

  • Dustinsfl
  • · Replies 2 ·
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2

Graduate Examples of ordered topology on R x R

  • Pippi
  • · Replies 4 ·
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4

Undergrad Real numbers as powers of real exponents

  • kulix
  • · Replies 16 ·
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Graduate What Does Unique Ring P Containing S Imply in Set Theory?

  • woundedtiger4
  • · Replies 3 ·
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Undergrad Why do all numbers in the complex plane define a unit circle radius?

  • rustynail
  • · Replies 6 ·
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6

Undergrad What is the value of f^{n}(x) when n approaches infinity?

  • Bipolarity
  • · Replies 5 ·
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Exhibit Function f Using Weierstrass Product Thm

  • Dustinsfl
  • · Replies 1 ·
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Graduate Trying to remember what Theorem this is.

  • Poopsilon
  • · Replies 4 ·
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4

Graduate Partial or Regular Derivative for Functional Derivative Stationary Value of 0?

  • delve
  • · Replies 2 ·
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High School My Professor frequently uses the term higher dimensions...

  • hivesaeed4
  • · Replies 2 ·
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Graduate Confusion about continuity and differentiability(In partial differential)

  • athrun200
  • · Replies 14 ·
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Graduate Can We Prove that an Open Ball is an Open Set Using Rectangles?

  • brydustin
  • · Replies 5 ·
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5

Undergrad What is the exact definition of a function?

  • woundedtiger4
  • · Replies 10 ·
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How to Prove the Sum of the Power Series Using the Series for Cotangent?

  • Dustinsfl
  • · Replies 5 ·
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5

Compute Residue of $\Gamma(z)$ at Negative Integers & 0

  • Dustinsfl
  • · Replies 3 ·
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3

Graduate Holder's inequality for integrals

  • brydustin
  • · Replies 9 ·
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9

Graduate Why does cantors theorem not prove the interval (0,1) in Q uncountable?

  • carheadford
  • · Replies 1 ·
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Graduate Convergent sequences in the cofinite topology

  • GridironCPJ
  • · Replies 1 ·
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Graduate Proof that Compact Subset of Metric Space is Bounded

  • Rasalhague
  • · Replies 2 ·
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2

Graduate Separable space definition and applications

  • Somefantastik
  • · Replies 2 ·
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2

Graduate Wierd sum of squares compilation to a single vector norm

  • Sorento7
  • · Replies 2 ·
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2

Express $\frac{1}{z+1}$ as a power series about z=1

  • Poirot1
  • · Replies 1 ·
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Graduate Finite Dimensional Hausdorff Topological Space

  • creative_
  • · Replies 5 ·
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Graduate Example of a Homeomorphism f: Q -> Q not order preseving or order-reversing

  • GridironCPJ
  • · Replies 11 ·
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Graduate The polarization identity in Hilbert space

  • AxiomOfChoice
  • · Replies 2 ·
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Graduate Are Metric Space Completions Topologically Equivalent?

  • Jamma
  • · Replies 3 ·
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3

Graduate Uncovering the Logic Behind Cl(A) = A

  • Rasalhague
  • · Replies 6 ·
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6

Graduate Riemann integrals and step functions

  • GridironCPJ
  • · Replies 1 ·
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Graduate Answer: Prove Oscillation of Subintervals in [c,d] with η < ω_f (x)

  • GridironCPJ
  • · Replies 6 ·
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What is the sum to infinity of this nearly geometric series?

  • Poirot1
  • · Replies 1 ·
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Graduate Is Limsup xk < ∞ if and only if the sequence {xk} is bounded above?

  • kingwinner
  • · Replies 8 ·
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Undergrad Fourier Series: Small Waves & Equal Amplitude

  • Emilijo
  • · Replies 10 ·
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Graduate Question about open sets in (-infinite,5]

  • dodo
  • · Replies 7 ·
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Analytic Isomorphism: Annulus vs. Punctured Unit Disc

  • Dustinsfl
  • · Replies 2 ·
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Undergrad Calculator operations and value of i.

  • Mholnic-
  • · Replies 12 ·
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Graduate Is this a homeomorphism that does not preserve metric completeness?

  • mathgirl313
  • · Replies 17 ·
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Analytic is UHP to unit disc

  • Dustinsfl
  • · Replies 9 ·
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9

Graduate Fourier series and Euclidean spaces

  • hamsterman
  • · Replies 4 ·
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4

Graduate Fourier series on a general interval [a, a + T]

  • glebovg
  • · Replies 5 ·
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5

Graduate Convergence in L^2 Norm: Understanding Subsequence Implications

  • AxiomOfChoice
  • · Replies 10 ·
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10

Undergrad Convergence/Divergence of a Series

  • d.tran103
  • · Replies 3 ·
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3

What books should I read to fill my knowledge gap in tensor analysis?

  • Fantini
  • · Replies 1 ·
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1

Graduate Dedekind Cuts Question (Conceptual)

  • mindarson
  • · Replies 1 ·
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1

Graduate Analysis question about continuity and vanishing functions

  • diligence
  • · Replies 3 ·
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3

Locus in the complex plane.

  • juantheron
  • · Replies 2 ·
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2

Graduate Why can't holomorphic functions be extended to a closed disc?

  • lugita15
  • · Replies 11 ·
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11

Prove that a function does not have a fixed point

  • Amer
  • · Replies 3 ·
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3

Prove F(x) Maps [0,1] into Itself and Not Contraction

  • Amer
  • · Replies 6 ·
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6

Find Complex Root of z^5=0 | Math Solutions

  • Amer
  • · Replies 3 ·
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3

What is the relationship between z and ω when |z| = |ω| = 1?

  • juantheron
  • · Replies 2 ·
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2

Undergrad Modulus of a Sequence: How to Prove Nullness?

  • rohan03
  • · Replies 2 ·
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2

Graduate Is Every Continuous Real-Valued Function on a Subset of R Bounded?

  • Useful nucleus
  • · Replies 9 ·
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Prove that a function has a fixed point

  • Amer
  • · Replies 7 ·
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7

Find Intersection of Complex Number Loci Given w

  • Punch
  • · Replies 5 ·
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5

Graduate Congruence as explained by Apostol in Calculus Volume 1.

  • glb_lub
  • · Replies 4 ·
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4

Conformal Mapping of Strip -1 < Im(z) < 1

  • Dustinsfl
  • · Replies 7 ·
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7

High School Difference between functional and function?

  • aditya23456
  • · Replies 4 ·
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4

Graduate Learn Topology with Our Ongoing Video Series - Perfect for All Levels!

  • QuanPenguin
  • · Replies 24 ·
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24

Complex Numbers VI: Finding Least Value of |z-2√2-4i|

  • Punch
  • · Replies 3 ·
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3

Find Abel Sum: Add 1 +1 -1 -1 +1 +1

  • alexmahone
  • · Replies 2 ·
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2

Solve Complex Number IV Problem: Find Radius & Centre

  • Punch
  • · Replies 5 ·
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5

Graduate Metric and completeness of real numbers

  • sunjin09
  • · Replies 6 ·
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6

Is the Harmonic Series a Counterexample to a Convergent Series?

  • alexmahone
  • · Replies 2 ·
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Fractional linear transformation--conformal mapping

  • Dustinsfl
  • · Replies 3 ·
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3

What Is the Correct Form of a Holomorphic Function on \(\mathbb{C}-\{0\}\)?

  • Dustinsfl
  • · Replies 1 ·
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1

Graduate Difference between hilbert space,vector space and manifold?

  • aditya23456
  • · Replies 9 ·
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9

Undergrad Are Finite Sets and the Set of All Integers in R^2 Closed?

  • jwqwerty
  • · Replies 12 ·
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12