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

Proving the limit of Lp norms ratio equals infinity norm

  • joypav
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1

Undergrad How to confirm the function has genus 116?

  • aheight
  • · Replies 3 ·
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3

Undergrad Completeness of a basis function

  • member 428835
  • · Replies 32 ·
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32

Undergrad Iterating powers of complex integers along axes of symmetry

  • Ventrella
  • · Replies 3 ·
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3

Undergrad Do partial derivatives commute in general?

  • jk22
  • · Replies 5 ·
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5

Graduate Derive Birkhoff Ergodic Theorem from Von Neumann

  • wrobel
  • · Replies 1 ·
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1

Graduate Structure preserved by strong equivalence of metrics?

  • lugita15
  • · Replies 2 ·
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2

Graduate Same open sets + same bounded sets => same Cauchy sequences?

  • lugita15
  • · Replies 2 ·
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2

Hubbard and Hubbard equation 1.7.10: limit sign change as h approaches 0

  • Math Amateur
  • · Replies 1 ·
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1

Finding border points and then interior points

  • A.Magnus
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1

Undergrad Trying to understand why a set is both open and closed

  • Mr Davis 97
  • · Replies 7 ·
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7

Find the square roots of 4*sqrt(3)+4(i)

  • Elissa89
  • · Replies 3 ·
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3

Undergrad Existence of Directional Derivative in Normed Linear Space

  • Gear300
  • · Replies 12 ·
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12

Convex Functions: Find $f,g$ Satisfying f(x)=g(x) iff x is an Integer

  • evinda
  • · Replies 9 ·
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9

Undergrad Topology Words: Reasons for the particular names

  • Cantor080
  • · Replies 2 ·
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2

Proving Convexity of $f: \mathbb{R} \to \mathbb{R}$

  • evinda
  • · Replies 1 ·
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1

Scalar projection vs norm of vector projection in Lovric's Theorem 1.6

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Open balls contained in other open balls

  • Mr Davis 97
  • · Replies 11 ·
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11

Undergrad Why does f(x)=x (x≤0) or 1+x (x>0) map open sets to open sets?

  • Robin04
  • · Replies 9 ·
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9

Undergrad Using the Baire Category theorem

  • Mr Davis 97
  • · Replies 2 ·
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2
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1

Proving Convergence of a Sequence with a Geometric Condition

  • evinda
  • · Replies 3 ·
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3

Finding the Limit Inferior and Limit Superior of a Sequence

  • evinda
  • · Replies 6 ·
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6

Show existence of subsequences

  • evinda
  • · Replies 4 ·
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4

Sequence has convergent subsequence

  • evinda
  • · Replies 2 ·
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2

Tu's theorem 2.2: tangent vectors as derivations at a point

  • Math Amateur
  • · Replies 2 ·
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2
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2

Why Can't Two Functions Cover the Unit Circle?

  • Math Amateur
  • · Replies 2 ·
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2

Lusin's Theorem - Infinite Measure and not Real-Valued Extensions

  • joypav
  • · Replies 1 ·
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1

Taylor's Theorem .... Loring W. Tu, Lemma 1.4 .... ....

  • Math Amateur
  • · Replies 2 ·
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2

What does vol₂ mean in Hubbard's geometric interpretation of k-forms?

  • Math Amateur
  • · Replies 2 ·
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2

Metric spaces and normed spaces

  • ozkan12
  • · Replies 4 ·
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4

Dot product projection in Bachman's 1-forms section

  • Math Amateur
  • · Replies 2 ·
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2

Understanding Lusin's Theorem for $\mathbb{R}$ and Its Proof

  • joypav
  • · Replies 1 ·
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1

How does ||a + t(a/||a||)|| = (||a|| - t)?

  • Math Amateur
  • · Replies 3 ·
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3

Abbott's theorem 6.5.1: why power series converges on R or bounded interval

  • Math Amateur
  • · Replies 2 ·
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2

Pointwise limit of x^(1/(2n-1)) in Abbott example 6.2.2

  • Math Amateur
  • · Replies 4 ·
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4

Evaluating i^(-21/2)

  • Asawira Emaan
  • · Replies 6 ·
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6

Graduate Analytical function from numerable point set

  • hilbert2
  • · Replies 6 ·
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6

Ap1.3.51 are complex numbers, show that

  • karush
  • · Replies 4 ·
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4

Undergrad Is every metric space homeomorphism an isometry?

  • facenian
  • · Replies 15 ·
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15

Undergrad Can we have a pasting lemma for uniform continuous functions

  • PKSharma
  • · Replies 2 ·
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2

Undergrad Hausdorff Metric: Definition 1 vs. Definition 2

  • Mr Davis 97
  • · Replies 1 ·
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1

Measure Theory - Existence of Fsigma set contained in measurable set

  • joypav
  • · Replies 1 ·
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1

Are Injective R-Linear Mappings in C Necessarily Surjective?

  • Math Amateur
  • · Replies 1 ·
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1

Law of cosines for complex numbers in Remmert section 1.3

  • Math Amateur
  • · Replies 1 ·
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1

How does Remmert derive the Cauchy-Schwarz Inequality in complex functions?

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad Flipping the sign in the definition of derivative

  • Mr Davis 97
  • · Replies 3 ·
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3

Undergrad Result regarding signs and a limit

  • Mr Davis 97
  • · Replies 3 ·
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3

Undergrad R-linear and C-linear mappings of C into C in Remmert

  • Math Amateur
  • · Replies 4 ·
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4

R-linear and C-linear mappings of ℂ into ℂ

  • Math Amateur
  • · Replies 3 ·
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3

High School Spivak's Calculus as a Prerequisite for General Topology

  • CaptainAmerica17
  • · Replies 25 ·
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25

Undergrad Complex differentiability implies real differentiability and C-linear differentials

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Does dim(M_α)=p when α is a wedge product of p vectors?

  • kiuhnm
  • · Replies 7 ·
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7

Complex and real differentiability in Remmert's theory of complex functions

  • Math Amateur
  • · Replies 1 ·
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1

Why is ln(k) a Complex Number When k is a Positive Integer?

  • highmath
  • · Replies 1 ·
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1

Graduate Is There a Unique Hodge Star Operator for Any p-Vector in Differential Forms?

  • kiuhnm
  • · Replies 2 ·
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2

Is e^x a transcendental function?

  • highmath
  • · Replies 5 ·
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5

Undergrad The Chain Rule for Multivariable Vector-Valued Functions ....

  • Math Amateur
  • · Replies 5 ·
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5

Chain rule theorem 12.7 proof in Apostol's Mathematical Analysis

  • Math Amateur
  • · Replies 2 ·
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2

Lafontaine's vector form of the differential definition

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad Metric Spaces and Topology in Analysis

  • Mr Davis 97
  • · Replies 1 ·
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1

Why is a multi-valued function considered a function?

  • highmath
  • · Replies 1 ·
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1

Graduate Show that set is an orthonormal set in PC(0,l)

  • Shackleford
  • · Replies 4 ·
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4

Equivalence of Shifrin's and Lafontaine's definitions of differentiability

  • Math Amateur
  • · Replies 4 ·
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4
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3

Directional derivative formula in Apostol 12.2 Example 4

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad How to prove that compact regions in surfaces are closed?

  • Gene Naden
  • · Replies 12 ·
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12

Properties of Functions of Bounded Variation

  • joypav
  • · Replies 3 ·
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3

Bounded Variation - Difference of Functions

  • joypav
  • · Replies 5 ·
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5

Proof of the norm inequality in Apostol's theorem

  • Math Amateur
  • · Replies 4 ·
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4

Using Rolle's theorem to prove for roots (part 2)

  • Joe20
  • · Replies 2 ·
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2

Undergrad Confused by the behavior of sqrt(z^2+1)

  • Measle
  • · Replies 6 ·
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6

Using Rolle's theorem to prove for roots

  • Joe20
  • · Replies 2 ·
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2

Continuous and differentiability

  • Joe20
  • · Replies 1 ·
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1
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6

Convergence and existence of constants

  • evinda
  • · Replies 6 ·
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6

Are my ideas as for the convergence right?

  • evinda
  • · Replies 6 ·
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6
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6

Doesn't it suffice to pick the limit of the sequence?

  • evinda
  • · Replies 4 ·
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4

Undergrad Showing that a_n > 0 given its decreasing and lim a_n=0

  • Mr Davis 97
  • · Replies 1 ·
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1

Undergrad Searcoid corollary 1.4.5 on ordinals and proper subsets

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad Can ordinals α and β be disjoint in Searcoid Theorem 1.4.6?

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Showing that an infinite sum converges when a sign in the denominator is flipped

  • Mr Davis 97
  • · Replies 11 ·
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11

Undergrad Limsup(a+b) = limsup(a) + limsup(b)

  • Mr Davis 97
  • · Replies 3 ·
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3

Undergrad Principal branch of the log function

  • Measle
  • · Replies 1 ·
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1

Undergrad Searcoid Theorem 1.4.4: minimality of β in α \ x

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Equality in the trichotomy for totally ordered ordinals

  • Math Amateur
  • · Replies 2 ·
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2

Finding Supremum and Infimum of Sets with Inequalities

  • evinda
  • · Replies 15 ·
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15

Undergrad How Do We Prove a Subset of an Ordinal is Well-Ordered?

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Series of even and odd subsequences converge

  • Mr Davis 97
  • · Replies 16 ·
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16

What is the Property of Infimum for Sets?

  • evinda
  • · Replies 8 ·
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8
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4

Problems for Cauchy Integral Formula

  • shirokuma
  • · Replies 1 ·
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1

Undergrad Learning the theory of the n-dimensional Riemann integral

  • AltairAC
  • · Replies 5 ·
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5

Is Φ a Bijective Map from Power Set to Characteristic Functions?

  • mathmari
  • · Replies 7 ·
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7

Undergrad How Is Divergence to Infinity Defined in Contrast to General Divergence?

  • Mr Davis 97
  • · Replies 3 ·
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3

Undergrad What does the edge of a Möbius strip look like when projected onto a 2D plane?

  • YoungPhysicist
  • · Replies 3 ·
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3

Undergrad Complex exponential to a power

  • Mr Davis 97
  • · Replies 4 ·
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4

Proving that solutions of a equation are irrational

  • ranga519
  • · Replies 2 ·
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2