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

The Union of Two Open Sets is Open

  • G-X
  • · Replies 3 ·
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3

Stromberg Theorem 3.47: why open set implies interval in intersection

  • Math Amateur
  • · Replies 2 ·
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2

What are the V_k in Stromberg's theorem 3.43?

  • Math Amateur
  • · Replies 2 ·
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2

TFAE proof involving limit and convergent sequence

  • brooklysuse
  • · Replies 2 ·
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2

Undergrad Proving a Fixed Point Theorem for Shrinking Maps on Compact Spaces

  • facenian
  • · Replies 8 ·
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8

High School Computing a tricky complex math problem - where did I go wrong?

  • Mayhem
  • · Replies 7 ·
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7

Why is the Weierstrass function continuous but nowhere differentiable?

  • mathmari
  • · Replies 38 ·
2
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38

Undergrad How do I create a sewing pattern for a spherical lune in 2D from an n-hosohedra?

  • Smed
  • · Replies 10 ·
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10

Graduate Definitions of Cylinder Sets and Cylinder Set Measure

  • leo.
  • · Replies 2 ·
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2

Undergrad Lindstrom Lemma 7.4.6: limit of integral over set B

  • Math Amateur
  • · Replies 6 ·
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6

Lindstrom Lemma 7.4.6: proving the limit inequality for integrals

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad How do I separate the real and imaginary parts of an infinite product?

  • benorin
  • · Replies 5 ·
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5

Undergrad Where is a list of Lehmer Pairs of zeros of zeta(s) ?

  • Swamp Thing
  • · Replies 2 ·
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2

Undergrad Lindstrom Proposition 7.3.7: sum of measurable functions

  • Math Amateur
  • · Replies 14 ·
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14

Lindstrom Proposition 7.3.7: sum of measurable functions

  • Math Amateur
  • · Replies 8 ·
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8

Undergrad What's the name of a 2-torus looped in the 4th dimension?

  • greswd
  • · Replies 8 ·
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8

Undergrad Do there exist surfaces whose boundary is a closed knot?

  • jk22
  • · Replies 3 ·
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3

Undergrad Reference For The Historical Context of Dedekind Cuts and Why the need

  • MidgetDwarf
  • · Replies 8 ·
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8

Prove Monotony of Function: $f$ Strictly Decreasing

  • awsomeman
  • · Replies 2 ·
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2

Graduate Choosing a graduate complex analysis textbook

  • benorin
  • · Replies 23 ·
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23

Undergrad Hölder and log-Hölder continuity

  • hilbert2
  • · Replies 2 ·
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2

Undergrad Self teaching analysis and topology

  • diegzumillo
  • · Replies 9 ·
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9

Undergrad Citation for a knot theory statement

  • BillKet
  • · Replies 3 ·
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3

Linear isometry from R² to C in Garling example 11.5.2

  • Math Amateur
  • · Replies 2 ·
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2

Proof of Corollary 11.4.3 in Garling's metric spaces book

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Nowhere diffferentable continuous function

  • mathman
  • · Replies 2 ·
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2

Undergrad Proving Willard theorem 3.11 part 1-a using closure-interior duality

  • Math Amateur
  • · Replies 2 ·
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2

Graduate How would you define a mathematical space?

  • TheDS1337
  • · Replies 11 ·
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11

Annihilator of a set in Garling's metric spaces

  • Math Amateur
  • · Replies 2 ·
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2
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2

Graduate Conformal Transformation as a diffeomorphism

  • radioactive8
  • · Replies 3 ·
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3

Cauchy-Schwarz equality condition in Garling 11.3.2

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Proving that the real projective plane is not a boundary

  • lavinia
  • · Replies 38 ·
2
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38
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2

Undergrad Proving X - E° = X - E closure in Willard

  • Math Amateur
  • · Replies 2 ·
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2

Insights The Analytic Continuation of the Lerch and the Zeta Functions

  • benorin
  • · Replies 0 ·
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0

Undergrad Is f(x) an Injective Function? Understanding Proof and Notation

  • CaptainAmerica17
  • · Replies 35 ·
2
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35

Local extremum at ξ when f''(ξ) ≠ 0 and f'(ξ) = 0

  • evinda
  • · Replies 11 ·
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11

Undergrad How does closure equality imply subset in Willard theorem 3.7?

  • Math Amateur
  • · Replies 5 ·
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5

Undergrad Fractional Integral of which function is equal to Riemann's Zeta-Function?

  • benorin
  • · Replies 2 ·
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2

Undergrad Reverse triangle inequality in Conway example 5.3.4(b)

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Indiscrete topology generated by trivial pseudometric

  • Math Amateur
  • · Replies 6 ·
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6

Open Sets in a Discrete Metric Space .... ....

  • Math Amateur
  • · Replies 2 ·
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2

Equivalence classes of open sets in Willard Example 2.7(a)

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Do Croom and Singh define local basis differently?

  • Math Amateur
  • · Replies 14 ·
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14

Undergrad Explanation that sin(x+iy) is one-to-one

  • hotvette
  • · Replies 2 ·
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2

Property of real-valued Fourier transformation

  • mathmari
  • · Replies 1 ·
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1

Undergrad Finding a non-convergent Cauchy sequence

  • Euler2718
  • · Replies 10 ·
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10

If f is convex and f(x) → ℓ, does f'(x) → 0?

  • mathmari
  • · Replies 23 ·
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23

Undergrad Order topology basis in Singh's Elements of Topology 1.4.4

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Coordinate Systems After Deformation of Axes

  • Opus_723
  • · Replies 2 ·
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2

Show that the two functions are identical

  • mathmari
  • · Replies 4 ·
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4

Undergrad Singh's description of topology generated by a subbasis

  • Math Amateur
  • · Replies 2 ·
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2

Laplace transform of -3e^{9t}+9sin(9t)

  • stephan2124
  • · Replies 2 ·
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2

Evaluating H(t-8)2cosh(t-8) with Heaviside function

  • dean2203
  • · Replies 2 ·
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2

Undergrad Why does complement of exceptional terms guarantee eventual equality in Singh 4.1.1?

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Why no rational is a limit of sequences in ℝ − ℚ

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Closure of constant function 1 on the complex set

  • victorvmotti
  • · Replies 11 ·
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11

Undergrad Convergence of a sequence of sets

  • benorin
  • · Replies 44 ·
2
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44

Undergrad Why does U in complement of A∪A' imply A∪A' is closed?

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Orthogonal complement of the orthogonal complement

  • victorvmotti
  • · Replies 4 ·
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4

Undergrad Closed subsets vs. elements of a topological space

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad Can Intuition be Used in Mathematics to Overcome Limit Laws and Norms?

  • Tucker121
  • · Replies 3 ·
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3

Undergrad Proving continuity definitions equivalent in Sutherland Chapter 8

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Functional equations as global formulas

  • Tendex
  • · Replies 17 ·
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17

Graduate Proof of Seifert-Van Kampen Theorem

  • PsychonautQQ
  • · Replies 2 ·
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2

Why does f(x) < 0 for x between β and b in Silva's IVT proof?

  • Math Amateur
  • · Replies 3 ·
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3

Graduate Questions about representation theory of Lie algebra

  • phoenix95
  • · Replies 5 ·
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5

Undergrad Example of a Lie group that cannot be represented in matrix form?

  • nrqed
  • · Replies 18 ·
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18

High School Something like an inverse Zeno's paradox

  • archaic
  • · Replies 11 ·
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11

Undergrad Continuity at b implies f(t) > y in Browder 3.16

  • Math Amateur
  • · Replies 4 ·
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4

Left continuity and the intermediate value theorem in Browder 3.16

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Proving continuity of f+ = max(f, 0) at zeros of f

  • Math Amateur
  • · Replies 18 ·
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18

Undergrad Why Isn't the Intersection of Two Lines a 1D Manifold?

  • nrqed
  • · Replies 21 ·
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21

Continuity of f^+ = max(f, 0) where f crosses zero

  • Math Amateur
  • · Replies 4 ·
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4

Relatively open sets in Stoll's Theorem 3.1.16

  • Math Amateur
  • · Replies 6 ·
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6

Undergrad Why does f⁻¹(U) ∩ f⁻¹(J) = f⁻¹(U) in Browder 3.12?

  • Math Amateur
  • · Replies 5 ·
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5

Undergrad Video lectures on lattices in mathematics

  • senmeis
  • · Replies 2 ·
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2

Proving A ≤ f(t) ≤ B for increasing functions in Browder 3.7

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Which class of functions does 1/x belong to?

  • SVN
  • · Replies 11 ·
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11

Graduate Conditions to extend functions Continuously into the Boundary (D^1/S^1)

  • WWGD
  • · Replies 7 ·
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7

Clarifying Conway's definition of continuity at a point

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Conway's proof of Proposition 2.1.2 on function limits

  • Math Amateur
  • · Replies 7 ·
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7

Undergrad Necessity condition in Browder theorem 5.10 on Riemann integrals

  • Math Amateur
  • · Replies 6 ·
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6

Conway Proposition 3.1.4: uniqueness of the Riemann integral

  • Math Amateur
  • · Replies 2 ·
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2

Differential of f(x,y) = (xy, x/y) using Browder proposition 8.12

  • Math Amateur
  • · Replies 2 ·
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2

Browder's proposition 8.12 on differentials in R^n

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Clenshaw-Curtis quadrature weights with even N collocation points

  • confused_engineer
  • · Replies 4 ·
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4

Undergrad Application of the Stone Weierstrass Theorem

  • CCMarie
  • · Replies 9 ·
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9

Partial fraction decomposition of a rational function with repeated poles

  • lucad93
  • · Replies 2 ·
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2

Browder Proposition 8.14: Why does r(tv)/t approach zero as t→0?

  • Math Amateur
  • · Replies 2 ·
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2

Why does Browder substitute h = tk in Definition 8.9?

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad The signal is binned into time bins with a width ##δt##

  • arcTomato
  • · Replies 4 ·
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4

Understand Andrew Browder's Prop 8.13: Math Analysis Introduction

  • Math Amateur
  • · Replies 2 ·
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2

Deriving f(p+h)−f(p)=Lh+r(h) from Browder's differentiability definition

  • Math Amateur
  • · Replies 2 ·
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2

High School Can you determine the size of a manifold globally from its Euclidean embedding?

  • sqljunkey
  • · Replies 10 ·
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10

Browder's remark on approximation by affine functions at a point

  • Math Amateur
  • · Replies 7 ·
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7

Understanding Andrew Browder's Prop 8.7: Operator Norm and Sequences

  • Math Amateur
  • · Replies 4 ·
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4

Understanding Proposition 8.7: Operator Norm and Sequences

  • Math Amateur
  • · Replies 4 ·
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4

Operator Norm and Distance Function .... Browder, Proposition 8.6 ....

  • Math Amateur
  • · Replies 2 ·
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2