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

Every Number is between Two Consecutuve Integers

  • OhMyMarkov
  • · Replies 2 ·
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2

Graduate Continuous Map to Single Point: Clarifying Confusion

  • dapias09
  • · Replies 3 ·
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3

Proving the Existence of Irrational Numbers Between Two Reals

  • OhMyMarkov
  • · Replies 5 ·
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5

Graduate When is a function equal to its Fourier series?

  • kloptok
  • · Replies 6 ·
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6

Undergrad Solving Sequences & Series: Limits & Sums

  • Bashyboy
  • · Replies 3 ·
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3

Fourier series without integration

  • Dustinsfl
  • · Replies 2 ·
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2

Show How to Prove Divergence of g'($\theta$)

  • Dustinsfl
  • · Replies 2 ·
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2

Differentiating a fourier series

  • Dustinsfl
  • · Replies 10 ·
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10

Graduate Is there a way to find a homeomorphism of the torus using a 2x2 integer matrix?

  • lavinia
  • · Replies 9 ·
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9

Graduate Another question about Fourier series convergence

  • Boorglar
  • · Replies 2 ·
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2

Undergrad Why Do We Have Different Terms for Least Upper Bound and Supremum?

  • back2square1
  • · Replies 3 ·
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3

Undergrad How Can We Prove the Global Minimum of the Absolute Value Function at x=0?

  • Bipolarity
  • · Replies 3 ·
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3

Proving b^r = sup(B(r)) for rational r using a proof by contradiction

  • poissonspot
  • · Replies 7 ·
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7
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4

Why Is the Function Bounded in the Extreme Value Theorem Proof?

  • Amer
  • · Replies 1 ·
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1

Graduate Pointwise Convergence of Fourier Series for a continuous function

  • Boorglar
  • · Replies 7 ·
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7

Graduate Uniform Convergence of Power Series

  • markiv
  • · Replies 6 ·
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6

A complex number problem that has been vexing me....

  • MarkFL
  • · Replies 2 ·
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2

Relationship between two entire functions

  • Bingk1
  • · Replies 4 ·
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4

Proving an entire function is a polynomial under certain conditions

  • Bingk1
  • · Replies 1 ·
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1

Responding to MF91's Claims on Real Numbers

  • VincentP
  • · Replies 3 ·
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3

Graduate Understanding Subset Equivalence in Lipschitz Equivalent Metrics Proof

  • PhysicsGente
  • · Replies 2 ·
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2

Graduate Continuous mappings in topology.

  • DeadOriginal
  • · Replies 9 ·
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9

Graduate Spivak's proof of A closed bounded subset of R^n is compact

  • middleCmusic
  • · Replies 2 ·
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2
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5

How to Solve the Heat Problem in the Disk using Fourier Series?

  • Dustinsfl
  • · Replies 1 ·
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1

Graduate Using the residue theorem to evaluate a real integral.

  • jrp131191
  • · Replies 2 ·
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2

On the Implication of Addition Axioms

  • OhMyMarkov
  • · Replies 4 ·
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4

Graduate Closed and open at the same time?

  • DeadOriginal
  • · Replies 20 ·
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20

Graduate Does Cl(X-A)=X-Int(A) work in infinite and uncountable dimensions?

  • cragar
  • · Replies 2 ·
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2

Closed sets intersection of countable open sets

  • Dustinsfl
  • · Replies 10 ·
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10

Accumulation Points of $(-1)^n + (1/m)$: Is it True?

  • Dustinsfl
  • · Replies 10 ·
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10

Graduate A question on the orthogonal polynomial

  • sufive
  • · Replies 2 ·
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2

Graduate Understanding lim sup and lim inf: Finding limit points and subsequential limits

  • funcalys
  • · Replies 2 ·
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2

Find Fourier Series for Piecewise Function

  • Dustinsfl
  • · Replies 3 ·
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3

What Are the Accumulation Points of the Sequence $1/n$?

  • Dustinsfl
  • · Replies 4 ·
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4
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2

Complex accumulation points and open/closed

  • Dustinsfl
  • · Replies 1 ·
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1

Accumulation Points of Rationals: Explained

  • Dustinsfl
  • · Replies 1 ·
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1

R^2 accumulation and open/closed

  • Dustinsfl
  • · Replies 1 ·
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1

Graduate Defining an upper/lower bound in lexicographically ordered C.

  • c0dy
  • · Replies 1 ·
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1

Solving Even Function Integrals: $a_0$ & $a_n$

  • Dustinsfl
  • · Replies 8 ·
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8

Calculating Fourier Coefficients for $f(\theta) = \theta^2$ on $[-\pi, \pi]$

  • Dustinsfl
  • · Replies 4 ·
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4

Understanding a question Fourier series

  • Dustinsfl
  • · Replies 1 ·
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1

Fourier Coefficients for $f(\theta) = \theta$

  • Dustinsfl
  • · Replies 1 ·
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1

Calculating Fourier Series of $f(\theta)$ on $[\pi, -\pi]$

  • Dustinsfl
  • · Replies 4 ·
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4

Proof: if f holomorphic then f(z)=λz+c

  • Seijo
  • · Replies 1 ·
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1

Graduate Bad proof in Fomin's Calculus of Variations?

  • genericusrnme
  • · Replies 1 ·
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1

Is $f$ a one-to-one function on $S$?

  • Dustinsfl
  • · Replies 4 ·
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4

Graduate Open sets preserved in linear transformation that isn't bijective?

  • dumbQuestion
  • · Replies 5 ·
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5

Are There Infinitely Many Rational Numbers Between Two Irrational Numbers?

  • Dustinsfl
  • · Replies 6 ·
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6

Undergrad What is the limit of (ah-1)/h as h approaches 0?

  • dumbQuestion
  • · Replies 4 ·
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4

Graduate How can we prove that the sum of alternating squares equals pi squared over 12?

  • psholtz
  • · Replies 6 ·
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6

Graduate Domain and range of complex functions

  • Avatrin
  • · Replies 3 ·
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3

Graduate Lebesgue topological dimension

  • hofhile
  • · Replies 2 ·
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2

Proving $\sum_{k=1}^{n}e^{ik\theta}$ Formula

  • Dustinsfl
  • · Replies 5 ·
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5

Supremum and Infimum of $S$: $a < b < c < d$

  • Dustinsfl
  • · Replies 4 ·
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4

Trig identities Fourier Analysis

  • Dustinsfl
  • · Replies 2 ·
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2

Undergrad Proving a known proof involving injection.

  • grjmmr
  • · Replies 1 ·
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1

Undergrad Understanding Function Notation in Higher Level Mathematics

  • Artimodes
  • · Replies 1 ·
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1

Special cases for sine and cosine sum

  • Dustinsfl
  • · Replies 3 ·
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3

Proving the Polynomial Identity for Dividing a^n-b^n by a-b

  • Dustinsfl
  • · Replies 4 ·
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4

Proving Sum of Cosines Simplifies to Trig Identity

  • Dustinsfl
  • · Replies 1 ·
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1

Proving the Basic Identity of Fourier Series

  • Dustinsfl
  • · Replies 1 ·
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1

Undergrad Bounded Sequence: Thomas-Finney Definition Explained

  • Ryuzaki
  • · Replies 1 ·
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1

Graduate Is the Nested Interval Theorem Flawed in My Textbook?

  • pyfgcr
  • · Replies 3 ·
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3

Graduate Topology, functional analysis, and group theory

  • -Alexander-
  • · Replies 1 ·
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1

Graduate Proof Error Q. Conway's Functions of One Complex Variable VI

  • julypraise
  • · Replies 4 ·
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4

Singularities of Complex Functions

  • timeforchg1
  • · Replies 2 ·
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2

Graduate Are Sigma Algebras Unique for a Given Set?

  • ChemEng1
  • · Replies 3 ·
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3

Graduate Spivak Exercice, Least Upper Bounds Chapter, Proof

  • c.teixeira
  • · Replies 3 ·
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3

Undergrad Understanding K-Convexity: Visualization and Intuitive Explanation

  • Constantinos
  • · Replies 1 ·
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1

Graduate Does Unconditional Convergence Apply to Infinite Subseries Partitions?

  • micromass
  • · Replies 1 ·
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1

Graduate Cardinalic flaw of Riemann integral

  • pyfgcr
  • · Replies 5 ·
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5

Graduate Showing Closed Subsets of Compact Sets are Compact

  • bedi
  • · Replies 8 ·
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8

Graduate The role of the Jacobian in the Implicit Function Theorem

  • Fractal20
  • · Replies 4 ·
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4

Graduate Proof of Lagrange multipliers method in calculus of variations.

  • chingel
  • · Replies 3 ·
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3

Graduate Calculus of Variation on Local Regions of Function Space

  • Viky553
  • · Replies 9 ·
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9

Graduate Why Are There No Interior Points in the Cantor Set?

  • bedi
  • · Replies 7 ·
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7

Undergrad The least upper bound property and the irrationals.

  • RediJedeye
  • · Replies 3 ·
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3

Graduate Why Can't a Sequence Have Two Distinct Limits in a Metric Space?

  • bedi
  • · Replies 4 ·
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4

Graduate Is a Concave, Nondecreasing, and Bounded Function on [0, ∞) Always Continuous?

  • hermanni
  • · Replies 11 ·
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11

Graduate Apply Lebesgue Integral: Examples & Explanations

  • woundedtiger4
  • · Replies 13 ·
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13

Graduate Precise definition of the limit of a sequence

  • srn
  • · Replies 3 ·
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3

Graduate Playing with Analytical Operators

  • LolWolf
  • · Replies 7 ·
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7

Graduate Q is dense in R question about proof

  • A_B
  • · Replies 5 ·
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5

Graduate Can complex numbers solve x^x = i and what is (-1)^{\sqrt{2}}?

  • limitkiller
  • · Replies 3 ·
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3

Graduate Conditional vs unconditional convergence

  • johnqwertyful
  • · Replies 2 ·
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2

Graduate What is Semidifferential Calculus?

  • Stephen Tashi
  • · Replies 3 ·
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3

Graduate Why Parseval's Identity Fails for Higher Exponents in Basel Problem

  • Boorglar
  • · Replies 9 ·
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9

Undergrad An Intuitive Understanding Vs. Analytic Proofs

  • vanmaiden
  • · Replies 2 ·
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2

Graduate Rudin Thm 2.41: E Closed & Bounded if Every Inf Subset Has a Lmt Pt

  • Dschumanji
  • · Replies 5 ·
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5

Graduate Countable versus uncountable infinities in math and physics

  • aikiddo
  • · Replies 3 ·
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3

Graduate Is it Possible for a Closed Disk to be Contained in an Open Set?

  • ashok vardhan
  • · Replies 1 ·
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1

Graduate Homeomorphisms with the discrete topology

  • Flying_Goat
  • · Replies 5 ·
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5

Graduate Difference between theorems 2.12 & 214 of Baby Rudin

  • prash_neo
  • · Replies 7 ·
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7

Lambert W Function: Solving $r=ue^u$

  • Dustinsfl
  • · Replies 1 ·
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1

Undergrad An algebraic property of complex numbers

  • AxiomOfChoice
  • · Replies 3 ·
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3

Graduate Sequence in Hilbert space,example

  • shotgun07
  • · Replies 2 ·
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2

What is the error bound in cubic spline approximation?

  • Amer
  • · Replies 1 ·
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1