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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Undergrad Understanding Dedekind Cuts: How to Recognize a Cut

  • mikeyBoy83
  • · Replies 2 ·
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Undergrad Product of complex conjugate functions with infinite sums

  • Adolfo Scheidt
  • · Replies 4 ·
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4

Undergrad Deformation of contour of integration or shifting poles

  • Frank Castle
  • · Replies 2 ·
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2

Convergence of Integrals: Exploring Methods and Challenges

  • mathmari
  • · Replies 11 ·
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11

How Do We Determine the Convergence of These Complex Integrals?

  • mathmari
  • · Replies 2 ·
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2

Laplace transform of a series in time t

  • sarrah1
  • · Replies 1 ·
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Undergrad Can 2D Vector Subspaces Form 3D Surfaces and How to Find Their Intersection?

  • rabbed
  • · Replies 16 ·
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Graduate Implicit function parameterization

  • rabbed
  • · Replies 16 ·
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16

Finding Taylor Polynomial for tan(x) - Wondering

  • mathmari
  • · Replies 32 ·
2
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32

Undergrad Question about Accumulation points

  • TheChemist_
  • · Replies 11 ·
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11

High School How Is Data Specifically Defined in Algebraic Topology?

  • dkotschessaa
  • · Replies 8 ·
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8

Undergrad Interior and closure in non-Euclidean topology

  • tomkoolen
  • · Replies 3 ·
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3

Undergrad Understanding the product topology

  • tomkoolen
  • · Replies 9 ·
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9

Undergrad What Defines a Piecewise Smooth Function?

  • Jehannum
  • · Replies 2 ·
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2

Is it possible to write this expression in the form $a+bi$?

  • Karpthulu912
  • · Replies 1 ·
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High School Complex Numbers in a Simple Example that I am Very Confused

  • Arman777
  • · Replies 5 ·
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5

Express Product In The Form a + bi

  • Karpthulu912
  • · Replies 4 ·
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4
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Graduate How to compute limit of removable singularity?

  • aheight
  • · Replies 7 ·
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7

Undergrad Metrics which generate topologies

  • Lucas SV
  • · Replies 5 ·
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5
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Prove or disaprove the statements

  • mathmari
  • · Replies 13 ·
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13

Undergrad Create algebraic function with finite power expansions?

  • aheight
  • · Replies 2 ·
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2

How could we show that D is bounded and closed?

  • mathmari
  • · Replies 4 ·
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4

Undergrad Constructing dimensions out of a graph structure?

  • FlorianDietz
  • · Replies 5 ·
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5

Undergrad Dense orbit and fixed point question

  • Zafa Pi
  • · Replies 16 ·
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Undergrad Simply-connected, complex, simple Lie groups

  • Rasalhague
  • · Replies 3 ·
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3

Undergrad Do Dedekind cuts fill the gaps in the rational number line?

  • FallenApple
  • · Replies 5 ·
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5

Undergrad Does analysis form a bridge to geometry?

  • FallenApple
  • · Replies 14 ·
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14

Finding Radius of Convergence for Series: n/2^n and 1/(4+(-1)^n)^3n

  • mathmari
  • · Replies 3 ·
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3

Undergrad Understanding the Complex Conjugate Property in Fourier Transform

  • arpon
  • · Replies 7 ·
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7

Undergrad Etymology of "regular" and "normal" spaces

  • dkotschessaa
  • · Replies 6 ·
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6

Undergrad What chapters of Munkres Topology are essential?

  • cpsinkule
  • · Replies 5 ·
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5

Graduate Handlebody and Knot composed of polygons

  • GEOPHILE2
  • · Replies 2 ·
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Undergrad What do I need to know to understand Uniform convergence?

  • MAGNIBORO
  • · Replies 8 ·
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Graduate Fundamental and Homology groups of Polygons

  • dkotschessaa
  • · Replies 15 ·
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15

Graduate Laplacian cylindrical coordinates

  • LagrangeEuler
  • · Replies 2 ·
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Is there a non-constant polynomial such that....

  • karseme
  • · Replies 3 ·
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Real Solutions of 4cos(e^x) = 2^x+2^-x: ln(2pi) < log2(2+sqrt3) < ln(3pi)

  • juantheron
  • · Replies 1 ·
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1

Undergrad Domain of single-valued logarithm of complex number z

  • goodphy
  • · Replies 2 ·
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2

Undergrad Prove -- The product of two compact spaces is compact

  • TeethWhitener
  • · Replies 6 ·
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6

Undergrad Proof check: S in C Compact implies S is closed and bounded

  • zellwwf
  • · Replies 1 ·
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1

Undergrad How can I prove that a sequence converges to a limit for every epsilon?

  • FallenApple
  • · Replies 4 ·
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4

Graduate Fourier transform and translational invariance

  • ShayanJ
  • · Replies 4 ·
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4

Limit of Sequence: Proving $b_0\in L(a_n)$ and Convergence Condition

  • mathmari
  • · Replies 3 ·
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Are These Limit Points, Limsup, and Liminf Correct for These Sequences?

  • mathmari
  • · Replies 4 ·
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4

Graduate Ortogonality of two variable functions

  • LagrangeEuler
  • · Replies 3 ·
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3

Graduate Complex conjugation in inner product space?

  • ATY
  • · Replies 2 ·
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2

Undergrad N-spherical coordinate angle intervals

  • TubbaBlubba
  • · Replies 5 ·
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5

Equation involving the inverse tangent function

  • karseme
  • · Replies 2 ·
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Undergrad Complex Analysis Harmonic functions

  • Alvis
  • · Replies 3 ·
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3

Prove that f(x)=cos(narccos(x)) is polynomial

  • karseme
  • · Replies 4 ·
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Are These Statements Equivalent to the Negation of a Bounded Sequence?

  • Mathick
  • · Replies 3 ·
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Undergrad What is the relationship between dot products and orthogonality of functions?

  • LLT71
  • · Replies 16 ·
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Graduate What Is the Correct Laurent Series for Cosine Functions with Inverse Arguments?

  • Mantella
  • · Replies 8 ·
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8

High School Uses of complex multiplication?

  • Prem1998
  • · Replies 21 ·
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Undergrad Limit of a product with bounded function

  • Austin Chang
  • · Replies 5 ·
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5

High School Inequalities of complex number

  • Einstein's Cat
  • · Replies 6 ·
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Graduate Proof of expansion of a certain value

  • dimitri151
  • · Replies 2 ·
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2

Prove that Q is not a finite set

  • issacnewton
  • · Replies 2 ·
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2

Undergrad Sketching Complex Numbers in the Complex Plane

  • MickeyBlue
  • · Replies 5 ·
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5

How to Evaluate the Integral of z(z+1)cosh(1/z) Over a Unit Circle?

  • brunette15
  • · Replies 2 ·
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Insights How to self study analysis. Part I: Intro analysis - Comments

  • micromass
  • · Replies 26 ·
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Undergrad Equivalence of two complex expressions

  • TheCanadian
  • · Replies 3 ·
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3

High School The rubber sheet analogy in Relativity

  • geordief
  • · Replies 4 ·
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Is the Supremum of the Sum of Two Sets Equal to the Sum of their Suprema?

  • alexmahone
  • · Replies 1 ·
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How do I complete this convergence proof?

  • alexmahone
  • · Replies 1 ·
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Use the formal definition to prove that the following sequence diverges

  • alexmahone
  • · Replies 1 ·
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1

Undergrad Drawing a Continuous Symmetrical Grid on a Sphere's surface

  • greswd
  • · Replies 12 ·
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12

Undergrad Can a CW complex exist without being a Hausdorff space?

  • viniciuslbo
  • · Replies 6 ·
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6

High School Intersecting Bivariate Functions: Is x=a the Only Point of Intersection?

  • Saracen Rue
  • · Replies 2 ·
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Undergrad Factoring a complex polynomial

  • TheCanadian
  • · Replies 1 ·
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Graduate Need help with peak deconvolution

  • Sheng2016
  • · Replies 4 ·
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4

Undergrad What is the conjugate of (A+iB)exp(C+iD)?

  • henry wang
  • · Replies 1 ·
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1

Graduate Can a Sphere Transform into a Donut?

  • Dopamine
  • · Replies 16 ·
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16

Square metric not satisfying the SAS postulate

  • pholee95
  • · Replies 3 ·
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3

Extreme points of L^p[0,1] on unit closed ball

  • Kokuhaku
  • · Replies 2 ·
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2

Undergrad Trying to understand the mistake in my logical reasoning

  • issacnewton
  • · Replies 12 ·
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12

Operator form of integro-differential equation

  • sarrah1
  • · Replies 2 ·
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2

Solving z^6=i for arguments between 90 and 180 degrees.

  • woof123
  • · Replies 2 ·
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2

Undergrad Completeness Property (and Monotone Sequence)

  • KT KIM
  • · Replies 4 ·
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4

Understanding Complex Number Math: |iz^2|

  • sweeper
  • · Replies 2 ·
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2

Test for Cauchy sequence (with limsup and log)

  • Kokuhaku
  • · Replies 5 ·
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5

Graduate What are the bounds of a ratio with a given set of numbers and variables?

  • iScience
  • · Replies 9 ·
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9

Undergrad Normed Vector Spaces and Topological Vector Spaces

  • Bashyboy
  • · Replies 9 ·
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9

How Do You Solve These Complex Logarithmic and Polynomial Equations?

  • Darken1
  • · Replies 3 ·
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3

Locus of Line Segment Mid Point Intercept Real/Imaginary Axis

  • juantheron
  • · Replies 3 ·
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3

Undergrad Help evaluating complex function in form m+ni?

  • NotASmurf
  • · Replies 10 ·
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10

Undergrad Does Continuity of F Affect the Maximal Solution Theorem?

  • Calabi
  • · Replies 1 ·
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1

About showing a function : not unbounded on B

  • bw0young0math
  • · Replies 4 ·
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4

High School What is the Error in Calculating (e^(iπ))^i?

  • Anonymous Vegetable
  • · Replies 14 ·
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Undergrad Isolating a complex-valued variable

  • TheCanadian
  • · Replies 2 ·
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2

Undergrad Magnetic field by infinite wire: convergence of integral

  • DavideGenoa
  • · Replies 2 ·
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2

Undergrad Limits of multivariable functions (uniform convergence)

  • JulienB
  • · Replies 7 ·
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7

Solve Fourier Transform: f(t)=sin(2πt)/t

  • lucad93
  • · Replies 2 ·
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2

Complex number as a root and inequality question

  • Darken1
  • · Replies 5 ·
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5

Undergrad Euler's Formula - Moving Particle Argument (Needham)

  • Math Amateur
  • · Replies 14 ·
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14

Graduate What is meant by "locally like a simplical complex?"

  • The Bill
  • · Replies 16 ·
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