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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6

Insights Complex and Irrational Exponents for the Layman - Comments

  • Isaac0427
  • · Replies 5 ·
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5

Graduate Can an n-dimensional object fit entirely in n-1 dimensions?

  • Einstein's Cat
  • · Replies 2 ·
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2

How can we show the existance of a ε?

  • mathmari
  • · Replies 2 ·
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2

Graduate Proof that log2(i) is rational but I think it is wrong

  • The UPC P
  • · Replies 5 ·
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5

Graduate Can Penrose Stairs Be Realized on a Torus?

  • mma
  • · Replies 18 ·
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18

Undergrad What is the Argument Principle in Complex Analysis?

  • Bruno Tolentino
  • · Replies 4 ·
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4

Graduate Gravity on a 1-D Torus: Understanding the Conceptual Simplification

  • ArielGenesis
  • · Replies 7 ·
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7

Help for test - functional analysis

  • simpleton1
  • · Replies 5 ·
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5

What is a Semigroup and How Does it Relate to Immeasurable Sets?

  • simpleton1
  • · Replies 13 ·
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13

Graduate How to Glue the Hyperbolic Plane to Form Klein's Quartic?

  • Lapidus
  • · Replies 6 ·
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6

Graduate Need some kind of convergence theorem for integrals taken over sequences of sets

  • benorin
  • · Replies 1 ·
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1

Graduate Is "Kirby's Problem List" fairly familiar to Knot Theorists?

  • dkotschessaa
  • · Replies 3 ·
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3

Graduate Finding the Origin of an Integral Identity | Numerical PDEs Homework

  • Brian T
  • · Replies 3 ·
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3

Insights Things Which Can Go Wrong with Complex Numbers - Comments

  • micromass
  • · Replies 3 ·
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3

Graduate Real Affine Plane: Definition & Properties

  • tgt
  • · Replies 2 ·
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2

Graduate Using complex description of div and curl in 2d?

  • Mappe
  • · Replies 1 ·
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1

Undergrad What is the meaning of ph(z) in complex numbers?

  • Fellowroot
  • · Replies 2 ·
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2

Graduate Does anybody know an introduction to Lie Algebra Bundles

  • fresh_42
  • · Replies 0 ·
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0

Graduate Finding Residue of Complex Function at Infinity

  • MartinKitty
  • · Replies 3 ·
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3

Please check this complex integral

  • ognik
  • · Replies 5 ·
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5

Complex numbers simplification

  • Guest2
  • · Replies 2 ·
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2

What is the ratio of complex numbers in the form of a question?

  • Guest2
  • · Replies 4 ·
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4

Quickest way to calculate argument of a complex number

  • Guest2
  • · Replies 3 ·
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3

Undergrad Factorizing an 'i' in Exponent: Justified?

  • Euler2718
  • · Replies 8 ·
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8

Please check this complex integral (#2)

  • ognik
  • · Replies 2 ·
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2

Prove: $(\sin \theta+ i \cos \theta)^8 = \cos 8\theta - i \sin 8\theta$

  • kaliprasad
  • · Replies 4 ·
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4

Graduate Proving Euler's Formula: A Rigorous Approach from First Principles

  • Astudious
  • · Replies 15 ·
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15

Graduate What is the relationship between Pi and curvature on different surfaces?

  • DaveC426913
  • · Replies 21 ·
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21

An expression resembling Laguerre

  • sarrah1
  • · Replies 2 ·
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2

Undergrad Graph isomorphism problem-advance in complexity research

  • marcus
  • · Replies 0 ·
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0

Is the Set K Convex and Does It Attain Its Euclidean Distance?

  • evinda
  • · Replies 1 ·
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1

Properties of Metric $\sigma(x,y)$

  • evinda
  • · Replies 5 ·
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5

The distance is attained by a unique point

  • evinda
  • · Replies 5 ·
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5

Graduate An automorphism in a Banach space

  • Calabi
  • · Replies 21 ·
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21

Graduate Lipschitz perturbations and Hammerstein integral equations

  • S.G. Janssens
  • · Replies 1 ·
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1

Undergrad Better definition for complex number

  • Bruno Tolentino
  • · Replies 41 ·
2
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41

Is the radius of convergence 1 or 1/2?

  • lucad93
  • · Replies 1 ·
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1
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2

Lorenz Attractor: Questions & Answers

  • dingo
  • · Replies 1 ·
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1

Graduate Knot Theory & Topology w/ Munkres & "The Knot Book" by Adams

  • dkotschessaa
  • · Replies 11 ·
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11

Graduate Overcoming Abstraction in Mathematics

  • Avatrin
  • · Replies 8 ·
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8

Rieman inversion formula in Laplace transform

  • lucad93
  • · Replies 1 ·
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1

Graduate Do Cauchy sequences always converge?

  • Calabi
  • · Replies 23 ·
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23

Undergrad What is different between "holds" and "holds true"?

  • bacte2013
  • · Replies 5 ·
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5

Graduate The union of any collection of closed sets is closed?

  • rhino1000
  • · Replies 7 ·
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7
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7

How does ${X}_{w}\subset {X^*}_{w}$ occur in modular metric space?

  • ozkan12
  • · Replies 6 ·
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6

Graduate References for Self Study in de Rham Cohomology

  • MissMoneypenny
  • · Replies 2 ·
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2
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4

Graduate Why is a branched line in R2 not a topological manifold?

  • CSteiner
  • · Replies 9 ·
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9

Graduate Complex Analysis: Conformal Mappings

  • JulieK
  • · Replies 3 ·
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3

Undergrad Why do those two terms add here?

  • Emilie.Jung
  • · Replies 3 ·
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3

Graduate Are Green's functions generally symmetric?

  • ShayanJ
  • · Replies 3 ·
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3

Graduate Hypergeometic function. Questions.

  • LagrangeEuler
  • · Replies 1 ·
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1

Good book recommendation on number systems.

  • Ackbach
  • · Replies 5 ·
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5

Graduate Prove A~B=>f(A)~f(B) for a continuous f:X->Y

  • BiGyElLoWhAt
  • · Replies 48 ·
2
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48

Limit of Absolute Values and Metric Spaces

  • ozkan12
  • · Replies 2 ·
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2

Is Every Sequence with a Cauchy Subsequence Also Cauchy?

  • ozkan12
  • · Replies 5 ·
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5

Graduate Is There a Flaw in the Symmetry Proof for Homology Classes?

  • BiGyElLoWhAt
  • · Replies 3 ·
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3

Understanding L^p Spaces: Origins and Applications

  • E01
  • · Replies 2 ·
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2

Graduate Why is ##\frac{1}{\sqrt{z}}## a branch point and ##\frac{1}{z}## a pole?

  • LagrangeEuler
  • · Replies 2 ·
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2

Graduate Understanding Complex Exponential Summation: How is the Arctan Function Used?

  • wirefree
  • · Replies 2 ·
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2

Graduate Motivation for geometrical representation of Complex numbers

  • Vinay080
  • · Replies 7 ·
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7

Undergrad How to Solve Equations with Complex Numbers

  • cdummie
  • · Replies 9 ·
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9

Undergrad Logic behind normal line in expressing plane

  • feryee
  • · Replies 10 ·
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10

Graduate Sequence is norm convergent implies it's strongly convergent

  • Chain
  • · Replies 4 ·
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4

Showing Completeness of Metric Spaces: Examples

  • evinda
  • · Replies 1 ·
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1

Undergrad Understanding the Closed Set of Natural Numbers

  • Parag Kulkarni
  • · Replies 8 ·
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8

Graduate Proving the Fundamental Group of SO(2) is Z: How Can it Be Done Explicitly?

  • Davidedomande
  • · Replies 5 ·
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5
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1

Graduate Fourier transform of function which has only radial dependence

  • LagrangeEuler
  • · Replies 7 ·
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7
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1

Undergrad Resources For Real Analysis and Concepts of Mathmatics

  • infinite.curve
  • · Replies 7 ·
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7

To prove that Cauchy sequence

  • ozkan12
  • · Replies 2 ·
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2

Limits of x* when n and m Approach Infinity

  • ozkan12
  • · Replies 2 ·
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2

How Can I Calculate the Norm of the Operator \(I-L^{-1}K\)?

  • sarrah1
  • · Replies 4 ·
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4

Triangle Inequality and Convergence of ${y}_{n}$

  • ozkan12
  • · Replies 4 ·
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4

Graduate What is the relation between unitary group, homotopy?

  • PRB147
  • · Replies 7 ·
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7

Can We Say "${y}_{n}=T{y}_{n-1}" in a Complete Metric Space?

  • ozkan12
  • · Replies 1 ·
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1

Undergrad Why do we need the set of complex numbers to solve?

  • astrololo
  • · Replies 43 ·
2
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43
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2

Graduate Complete set of multi-variable functions

  • ShayanJ
  • · Replies 3 ·
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3

Graduate Proving Isomorphism of Linear Operator with ||A|| < 1

  • Jaggis
  • · Replies 6 ·
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6

Graduate What Is Conformal Mapping in Complex Analysis?

  • PhysicsKid0123
  • · Replies 6 ·
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6

Find Continuous Functions Subject to an Integral Condition

  • evinda
  • · Replies 1 ·
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1

Graduate Unbounded operator and expansion of commutator

  • ShayanJ
  • · Replies 19 ·
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19

Greens Function for Hemmholtz using Fourier

  • ognik
  • · Replies 1 ·
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1

How do we find A0 in Fourier series for f(x)=x?

  • ognik
  • · Replies 5 ·
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5

Greens function has me blue ....

  • ognik
  • · Replies 1 ·
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1

Undergrad Analysis and how to solve things (methods)

  • gillouche
  • · Replies 4 ·
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4

Undergrad Quantity of Vertices, Edges, Etc In Higher Dimensional Cubes

  • Richard Craig
  • · Replies 2 ·
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2

What is the complex number C for the transformation T?

  • avyunker
  • · Replies 1 ·
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1

Graduate How to make a 2-sphere in 4 dimensions

  • jk22
  • · Replies 21 ·
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21

Graduate How can we parameterize the cycloid traced by a rolling circle?

  • mathmari
  • · Replies 11 ·
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11

Find a parametrization of the following level curves

  • evinda
  • · Replies 33 ·
2
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33

Graduate Complex integral for z-transform causality

  • thegreenlaser
  • · Replies 4 ·
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4

Cartesian Equation for Parametrized Curve: Find Solution

  • evinda
  • · Replies 8 ·
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8

How to Calculate Distances from Foci to Tangent Line on an Ellipse?

  • mathmari
  • · Replies 1 ·
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1

Graduate Notation question for probability measures on product spaces

  • economicsnerd
  • · Replies 5 ·
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5