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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Graduate Open sets in R being the union of open intervals

  • wisvuze
  • · Replies 2 ·
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Graduate How to show induced topological space

  • ismaili
  • · Replies 3 ·
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3

Graduate Continuity in Half Interval Topology for x^2 Function

  • Slats18
  • · Replies 10 ·
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10

Graduate Add 2 Dense Sets for Non-Dense Set Result

  • cragar
  • · Replies 32 ·
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Graduate Relations between curvature and topology

  • joseph0086
  • · Replies 2 ·
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2

Graduate Finding J where logb(J) = -b for all b

  • Frogeyedpeas
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3

Undergrad Why does (e^{i\alpha})^2 always equal 1?

  • Piano man
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3

Graduate Can say me why annulus and circle are not homeomorphic?

  • seydunas
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2

Graduate Paracompactness and metrizable manifolds

  • aleazk
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2

Undergrad What is a compact space in topology?

  • lavster
  • · Replies 4 ·
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4

Graduate Do Homeomorphisms , Diffeomorphisms Preserve Intersections?

  • Bacle
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2

Graduate Is the human body topologically equivalent to a donut with multiple holes?

  • DaveC426913
  • · Replies 19 ·
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19

Graduate What is a Complete Metric Space in Mathematics?

  • Amok
  • · Replies 3 ·
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3

Graduate Can Probability and Topology Combine for an Exciting Research Topic?

  • Paparazzi
  • · Replies 6 ·
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6

Is the close interval A=[0,1] is compact?

  • rohan302
  • · Replies 3 ·
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3

Graduate I'm trying to find all functions such that Re(f(z)) + Im(f(z)) = 0, or

  • Char. Limit
  • · Replies 9 ·
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9

Graduate Discretized complex exponential

  • cepheid
  • · Replies 2 ·
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2

Graduate Proof of Topology: Compact Subsets in Open Sets

  • ForMyThunder
  • · Replies 2 ·
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2

Undergrad Computing (√3+i)^2010 without De Moivre's theorem

  • Chuckster
  • · Replies 6 ·
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6

Graduate Solving (-2)^(1/2) and (-2)^(1/sqrt(pi)): A Complex Analysis Approach

  • davedave
  • · Replies 2 ·
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2

Graduate Is the set of convergent sequences larger than convergent series?

  • Char. Limit
  • · Replies 7 ·
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7

Undergrad Complex numbers an Pythagoras' theorem.

  • JDude13
  • · Replies 9 ·
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9

Graduate So, what is the principal value of i^{3i}?

  • hbweb500
  • · Replies 2 ·
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2

Graduate How to abelianizing the fundamental group?

  • kakarotyjn
  • · Replies 3 ·
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3

Graduate How Can a Finite Set of Natural Numbers Be an Open Set in Topology?

  • 0ddbio
  • · Replies 2 ·
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2

Undergrad Solving (a+bi)/(-a+bi)=c+di for a and b

  • commander22
  • · Replies 2 ·
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2

Graduate Embedding Complex Matrices into Real Spaces

  • Kreizhn
  • · Replies 5 ·
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5

Graduate R^2 and R^2 - {(0,0)} are not homeomorphic

  • poet_3000
  • · Replies 7 ·
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7

Undergrad Understanding Complex Numbers: A Visual Explanation

  • QuarkCharmer
  • · Replies 1 ·
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1

Graduate Can the value of a function at a point of discontinuity vary among authors?

  • spaghetti3451
  • · Replies 5 ·
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5

Graduate Open set (differential equation)

  • stanley.st
  • · Replies 1 ·
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1

Graduate Relationship b/w Connectedness and Homeomorphisms

  • rekovu
  • · Replies 3 ·
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3

Graduate Does the boundedness inequality alone imply a linear operator?

  • mathplease
  • · Replies 6 ·
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6

Graduate How to represent a fraction infinitely close to 1?

  • Alan1000
  • · Replies 18 ·
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18

Graduate Topological and Metric Properties

  • Bachelier
  • · Replies 3 ·
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3

Graduate Cauchy Sequences in General Topological Spaces

  • ebola1717
  • · Replies 2 ·
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2

Graduate Continuous functions that vanish at infinity

  • Fredrik
  • · Replies 28 ·
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28

Graduate Finite cartesian product of connected space is connected

  • princy
  • · Replies 7 ·
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7

Graduate Topology and the Chinese Remainder Theorem?

  • ForMyThunder
  • · Replies 2 ·
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2

Graduate Prove Metric Theorem: (X,d) x B(x,δ) ⊆ B(x,ϵ)

  • thraxrules
  • · Replies 2 ·
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2

Graduate Why is every compact space locally compact?

  • winmath
  • · Replies 3 ·
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3

Graduate .999 = 1, in descrete topology?

  • TylerH
  • · Replies 4 ·
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4

Graduate Properties of Homeomorphisms between topological spaces

  • Goldbeetle
  • · Replies 9 ·
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9

Undergrad Raising Complex Numbers to Powers of Angles - What Happens?

  • Andrea2
  • · Replies 2 ·
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2

Graduate Topology Problem: Closure X Path-Connected?

  • mveritas
  • · Replies 3 ·
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3

Graduate Does a diffeomorphism between regions imply homeomorphism?

  • Pinu7
  • · Replies 5 ·
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5

Graduate Differentiating a Linear Functional

  • Kreizhn
  • · Replies 3 ·
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3

High School Complex numbers - parallel lines meet at infinity ? What does it mean?

  • Femme_physics
  • · Replies 3 ·
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3

Graduate Polyhedron of a simplicial complex and identification topology

  • kakarotyjn
  • · Replies 5 ·
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5

Graduate Non 2nd-countable, Hausdorff, differentiable n-manifold?

  • RoNN|3
  • · Replies 17 ·
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Graduate Afraid to Manipulate Complex Numbers

  • nonequilibrium
  • · Replies 1 ·
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Graduate How Does Raising e^(2*pi*i) = 1 to the Power of 1/(2*pi*i) Work?

  • nameonascreen
  • · Replies 5 ·
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5

Graduate A simple functional derivative

  • sprik
  • · Replies 1 ·
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Graduate Is accumulation point = adherent point in a closed set?

  • kadas
  • · Replies 2 ·
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2

Graduate Product Topology and Compactness

  • Bleys
  • · Replies 2 ·
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2

Graduate Which collections of subsets of R are bases for a topology?

  • Damascus Road
  • · Replies 14 ·
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14

Undergrad Simple but frustrating confusion on definition of bounded function

  • HJ Farnsworth
  • · Replies 4 ·
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4

Graduate Example of dense non surjective operator

  • ak416
  • · Replies 1 ·
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1

Graduate What Does It Mean for a Function to Have Compact Support?

  • mnb96
  • · Replies 2 ·
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2

Graduate Questions about hyperreal numbers/functions

  • lolgarithms
  • · Replies 12 ·
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12

Graduate Why do squares with center P satisfy the given equations in Putnam A1?

  • john562
  • · Replies 3 ·
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3

Graduate Define Metric for Set of Reals in n Dimensions

  • TylerH
  • · Replies 6 ·
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6

Graduate Why use a laurent series in complex analysis?

  • ENgez
  • · Replies 3 ·
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3

Graduate Proving Bounded Open Sets Union of Disjoint Open Intervals

  • Gear300
  • · Replies 4 ·
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4

Graduate What Connects the Natural Logarithm of i with Pi?

  • zketrouble
  • · Replies 20 ·
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20

Graduate Split-complex numbers and dual numbers

  • ForMyThunder
  • · Replies 1 ·
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1

Undergrad Is the equality \sqrt[n]{ab}= \sqrt[n]{a}\sqrt[n]{b} true for complex numbers?

  • gabel
  • · Replies 10 ·
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10

Graduate Neither of those is a real number, much less a positive real number.

  • Bob Busby
  • · Replies 5 ·
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5

Graduate Hilbert Space Orthonormal Sets: Alternative to Rudin

  • Hjensen
  • · Replies 3 ·
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3

Graduate [Proof] Fourier Coefficients = zero => function zero

  • nonequilibrium
  • · Replies 5 ·
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5

Undergrad Is 2.999... equal to 3?

  • Little ant
  • · Replies 20 ·
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20

Graduate Why does i have no properties that distinguish it from -i?

  • Yayness
  • · Replies 47 ·
2
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Undergrad How to eliminate imaginary parts of complex expression?

  • kaizen.moto
  • · Replies 3 ·
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3

Graduate Dynamic Programming Related Questions

  • sampahmel
  • · Replies 3 ·
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3

Graduate Can Achilles Catch the Tortoise Without the Continuum Property?

  • Rasalhague
  • · Replies 3 ·
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3

Graduate Can you explain me how these equations were obtained?

  • whuzzwhuzz
  • · Replies 3 ·
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3

Graduate Interiors of sets in topological vector spaces

  • AxiomOfChoice
  • · Replies 1 ·
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1

Graduate How Do You Prove the Bolzano-Weierstrass Theorem?

  • maximus101
  • · Replies 3 ·
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3

Graduate Complex numbers representing Real numbers

  • DrummingAtom
  • · Replies 3 ·
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3

Graduate Are there imaginary numbers other than i?

  • filter54321
  • · Replies 14 ·
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14

Undergrad Does subtraction of functions have meaning when functions are written symbolically?

  • Abu Rehan
  • · Replies 3 ·
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3

Undergrad Extension of the Triangle Inequality

  • Caspian
  • · Replies 2 ·
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2

Graduate Why not represent 3D space with one complex dimension for four dimensions

  • closet mathemetician
  • · Replies 1 ·
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1

Undergrad What is the Meaning of Re(function)?

  • nkk2008
  • · Replies 3 ·
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3

Graduate Are Fourier transforms unique?

  • pellman
  • · Replies 5 ·
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5

Graduate Open set challenging question and mind-blogging conceptWelcome.

  • kntsy
  • · Replies 17 ·
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17

Undergrad What are complex functions and how can they be graphed?

  • madah12
  • · Replies 5 ·
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5

Graduate What is the Locus of Roots in a Cubic Equation with Complex Numbers?

  • jammed
  • · Replies 10 ·
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10

Graduate Dividing both sides by a Dirac delta function - ok?

  • pellman
  • · Replies 2 ·
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2

Graduate Why are there no positive infinitesimals in the reals?

  • Rasalhague
  • · Replies 14 ·
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14

Graduate Nested intervals and unique determination in Courant

  • osnarf
  • · Replies 8 ·
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8

Graduate What is in the distributional sense ?

  • inlaid
  • · Replies 12 ·
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12

Graduate How can f(x, y) be defined on y=x for a continuous function?

  • Alexx1
  • · Replies 2 ·
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2

Graduate Cartesian product of R^n and R^m

  • JG89
  • · Replies 4 ·
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4

Graduate What do you think about Lang Textbooks?

  • dreamtheater
  • · Replies 1 ·
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1

Graduate Reading Haaser-Sullivan's Real Analysis

  • _DJ_british_?
  • · Replies 3 ·
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3

Graduate Is the equation z^z + 1 = 0 solvable?

  • mechprog
  • · Replies 12 ·
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12

Graduate Rotating two different complex numbers

  • daniel_i_l
  • · Replies 2 ·
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2

Undergrad Graphical representation of complex roots to equations

  • RK1992
  • · Replies 3 ·
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3

Graduate Reiman sphere mobius transforms and inverse square

  • zwoodrow
  • · Replies 1 ·
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1