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

High School Is the Geometry/Topology of Mazes a thing?

  • DaveC426913
  • · Replies 18 ·
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18

Proving Relatively Compactness in C([a, b]) using Arzelá-Ascoli Theorem

  • fabiancillo
  • · Replies 2 ·
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2

Prove that it converges uniformly

  • fabiancillo
  • · Replies 2 ·
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2

Undergrad Functions.wolfram.com accepted and published my formula for Gamma Fn

  • benorin
  • · Replies 11 ·
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11

Undergrad Proving a convergent sequence is bounded

  • cbarker1
  • · Replies 3 ·
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3

Undergrad How Does Fourier Transform Analyze Beats in Signals?

  • Salmone
  • · Replies 7 ·
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7

Undergrad Proof of Induction Principle starting from N, not from 1

  • Hall
  • · Replies 6 ·
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6

Undergrad Looking for an expert on integrals

  • benorin
  • · Replies 0 ·
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0

How do I use the definition to find a limit of a sequence?

  • slwarrior64
  • · Replies 2 ·
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2

Graduate Pontrjagin classes in cohomology with coefficient rings

  • quasar987
  • · Replies 4 ·
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4

Insights The Orin Fractional Calculus

  • benorin
  • · Replies 9 ·
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9

How Do Riemann Integrals Handle Function Splits and Summations?

  • evinda
  • · Replies 2 ·
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2

Undergrad Looking for Someone Strong in Analysis

  • benorin
  • · Replies 12 ·
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12

Insights The Extended Riemann Hypothesis and Ramanujan’s Sum

  • fresh_42
  • · Replies 3 ·
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3

Graduate Measure of non-periodicity of almost periodic functions

  • reterty
  • · Replies 1 ·
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1

Recursive Function for Virus Spread: Finding the General Solution

  • Tekilou
  • · Replies 3 ·
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3

Undergrad Hopf Fibration, torus with fibers, do it 2 ways?

  • Spinnor
  • · Replies 14 ·
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14

Proving Lemma 3.3 of L&S: Further Aspects of the Proof

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad What's the definition of "periodic extension of a function"?

  • CGandC
  • · Replies 14 ·
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14

Undergrad Show that (0, ∞) is homeomorphic to (0, 1)

  • Mikaelochi
  • · Replies 6 ·
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6

Undergrad The behavior of a potential-like integral at infinity

  • wrobel
  • · Replies 21 ·
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21

Infinite series involving 'x' has a constant value

  • SatyaDas
  • · Replies 3 ·
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3

Riemann integrable functions with compact support on D&K pages 427-428

  • Math Amateur
  • · Replies 2 ·
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2

How can we prove the inequality for the supremum and infimum of f*g and f*g?

  • Math Amateur
  • · Replies 2 ·
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2

Finding B' in Proposition 6.1.2 for n=2 in Duistermaat-Kolk

  • Math Amateur
  • · Replies 4 ·
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4

Complex Analysis: Does $\int_{C(0,10)} f(z)$ Equal 0?

  • mathmari
  • · Replies 2 ·
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2

Undergrad In Euclidian space, closed ball is equal to closure of open ball

  • CGandC
  • · Replies 7 ·
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7

Undergrad Duistermaat–Kolk Prop. 6.1.2: volume additivity with overlapping rectangles

  • Math Amateur
  • · Replies 22 ·
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22

Graduate Hausdorff property of projective space

  • Korybut
  • · Replies 9 ·
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9

Graduate Understanding Cantor set C in Ternary form with 1/n factor in front C

  • cbarker1
  • · Replies 4 ·
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4

Undergrad Describing homeomorphisms with the π1 function

  • Mikaelochi
  • · Replies 2 ·
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2

Graduate DMD is better without Ergodic Theory and Koopman Operators

  • AcademicOverAnalysis
  • · Replies 2 ·
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2

Undergrad Brunnian links with lark's-head knots instead of standard rubberband loops

  • egmoen
  • · Replies 4 ·
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4

A function given by a logical expression write in the truth table.

  • vokan12
  • · Replies 2 ·
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2

Undergrad Writing down an explicit homotopy

  • Mikaelochi
  • · Replies 4 ·
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4

High School Is there a function for every possible "path"?

  • Jurgen M
  • · Replies 19 ·
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19

Undergrad "Approximating Basis" -- Is there a contemporary term?

  • Ziva
  • · Replies 9 ·
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9

Undergrad Why Does the Complex Conjugate Involve Negating the Argument Theta?

  • Leo Liu
  • · Replies 9 ·
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9

Undergrad Broadly spiralling shape from partial sums of Zeta (0.5 + i t)

  • Swamp Thing
  • · Replies 8 ·
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8

Undergrad Showing that a group acts freely and discretely on real plane

  • kmitza
  • · Replies 5 ·
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5

High School Is the Quotient Topology of Real Numbers Homeomorphic to Real Numbers?

  • Korybut
  • · Replies 6 ·
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6

Undergrad Is zero set aposyndetic equivalent to aposyndetic?

  • kmitza
  • · Replies 2 ·
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2

Graduate Limits and Supremum: Is It True?

  • Mathvsphysics
  • · Replies 3 ·
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3

High School What kind of definition is this?

  • mcastillo356
  • · Replies 23 ·
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23

Does This Sequence Converge Uniformly?

  • mathmari
  • · Replies 4 ·
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4
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2

High School Why Is the Trick for Open Sets in Quotient Topology Valid?

  • Korybut
  • · Replies 8 ·
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8

Undergrad Doing proofs with the variety function and the Zariski topology

  • Mikaelochi
  • · Replies 5 ·
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5

Undergrad A problem of completeness of a metric space

  • facenian
  • · Replies 3 ·
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3

Undergrad Proving a function f is continuous given A U B = X

  • Mikaelochi
  • · Replies 5 ·
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5

Undergrad Solving Zeno's Paradox: The Flaw in the Notion of Infinity

  • Chris S
  • · Replies 46 ·
2
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46

Undergrad Show R² \ {(0,0)} and the annulus 1 < √(x²+y²) < 3 are homeomorphic

  • Mikaelochi
  • · Replies 8 ·
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8

High School Can we have a complex number in the exponent?

  • docnet
  • · Replies 2 ·
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2

Determine the area, calculate the basis vectors and determine the inner product

  • Karl Karlsson1
  • · Replies 2 ·
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2

Undergrad An open set can be a closed interval?

  • Demystifier
  • · Replies 12 ·
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12

Extrema and convergence of sequence

  • mathmari
  • · Replies 9 ·
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9

Calculate the volume of the set M

  • mathmari
  • · Replies 7 ·
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7

What percentage is 60 million of 60 billion?

  • apw
  • · Replies 2 ·
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2

Need help with topology or analysis

  • jaychay
  • · Replies 3 ·
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3

Limit comparison test

  • jaychay
  • · Replies 11 ·
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11

Graduate Topological Data Analysis - Persistent Homology

  • phys_student1
  • · Replies 8 ·
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8

High School Real numbers and complex numbers

  • grzz
  • · Replies 38 ·
2
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38
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3

Cauchy-Riemann Equations test problem

  • jaychay
  • · Replies 6 ·
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6

Help with harmonic function problem

  • jaychay
  • · Replies 2 ·
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2

Undergrad Continuity of an inverse of a function

  • archaic
  • · Replies 2 ·
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2

Help with complex number function problems

  • jaychay
  • · Replies 12 ·
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12

Complex number equation graph problem

  • jaychay
  • · Replies 12 ·
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12

Global Extrema of a Trigonometric Function

  • mathmari
  • · Replies 16 ·
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16

No Real Zeroes of $x^6-x^5+x^4-x^3+x^2-x+\dfrac{3}{4}$

  • anemone
  • · Replies 1 ·
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1

Expanding open sets and shrinking closed sets in Carothers 16.1

  • Math Amateur
  • · Replies 2 ·
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2

High School What is the nature of dimensionality in 11 dimension M-theory?

  • Paige_Turner
  • · Replies 2 ·
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2

Undergrad Pseudometric Spaces: What Are They and Why Are They Important in Mathematics?

  • Paige_Turner
  • · Replies 9 ·
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9

Graduate Is the Assertion Derived from a General Theorem Trivial or Interesting?

  • wrobel
  • · Replies 0 ·
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0

Finding the Unique Solution of a Polar System with Variable Radius?

  • Jiggerjaw
  • · Replies 2 ·
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2

Undergrad Negative curvature in low dimensions

  • Paige_Turner
  • · Replies 3 ·
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3

Undergrad Is there a "Nice" proof that R^2 is not disconnected when we remove 2 points

  • WWGD
  • · Replies 3 ·
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3

Graduate What Are n-Dimensional Holes in Topology?

  • WWGD
  • · Replies 5 ·
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5

Verifying topology axioms for ℝ ∪ {★} with custom open sets

  • mathmari
  • · Replies 2 ·
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2

Undergrad Regarding i^2, and why it's -1 and not 1

  • Grasshopper
  • · Replies 45 ·
2
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45

Undergrad Maximal collection with FIP and T₁ separation axiom

  • facenian
  • · Replies 7 ·
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7

Graduate How Do You Determine the Mapping Functions in a Curvilinear Coordinate System?

  • zaki
  • · Replies 2 ·
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2

Prove that series converges uniformly

  • fabiancillo
  • · Replies 3 ·
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3

Prove that the algebra generated is dense

  • fabiancillo
  • · Replies 2 ·
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2

Correctness of Statements about Set A in Metric Space X

  • mathmari
  • · Replies 32 ·
2
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32

Graduate Fourier transform of hyperbolic tangent

  • jjr
  • · Replies 6 ·
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6

Prove/Disprove: Uniform Continuity of sin(sin(x))

  • solakis1
  • · Replies 4 ·
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4

F doesn't have in (0,0) a local minimum

  • mathmari
  • · Replies 4 ·
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4

Points of the surface with minimum distance to the point (3,0,0)

  • mathmari
  • · Replies 4 ·
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4
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32

F convex iff Hessian matrix positive semidefinite

  • mathmari
  • · Replies 24 ·
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24

What Are Level Lines and Gradients in Multivariable Calculus?

  • mathmari
  • · Replies 22 ·
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22

Is f Differentiable at (0,0)?

  • mathmari
  • · Replies 8 ·
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8

Undergrad Angles between complex vectors

  • Physgeek64
  • · Replies 3 ·
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3

Can the Sum of Two Squares Ever Equal 3 Times a Perfect Square?

  • MathLover_James
  • · Replies 2 ·
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2

Partial derivatives of piecewise function with x^2sin(1/x) terms

  • mathmari
  • · Replies 21 ·
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21

F is partially differentiable in (0,0) but not total differentiable

  • mathmari
  • · Replies 11 ·
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11

Finding the Infimum and Supremum

  • slwarrior64
  • · Replies 4 ·
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4

Undergrad ##(a_n) ## has +10,-10 as partial limits. Then 0 is also a partial limit

  • CGandC
  • · Replies 13 ·
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13

Graduate Is There a Simple Method to Analyze the Boundary of the 3-Sphere?

  • jk22
  • · Replies 43 ·
2
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43