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 Non-trivial field limits' equivalence?

  • Loren Booda
  • · Replies 9 ·
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9

Graduate Describing a Cyclic Space: 0 = 1

  • yetar
  • · Replies 2 ·
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2

Undergrad Square Root of Complex Numbers

  • littleHilbert
  • · Replies 5 ·
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5

Undergrad What Distinguishes Distributions from Functions?

  • Swapnil
  • · Replies 2 ·
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2

Undergrad How to compare complex numbers with greater than

  • Teegvin
  • · Replies 7 ·
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7

Graduate Proving the Independence of Connected Sum on Open Discs: A Topological Approach

  • Diophantus
  • · Replies 2 ·
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2

Graduate Fundamental Groups of the Mobius Band

  • Palindrom
  • · Replies 6 ·
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6

Graduate Does continuity of an invertible function imply continuity of its inverse?

  • quasar987
  • · Replies 2 ·
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2

Undergrad What is the second part of the question asking?

  • phalanx123
  • · Replies 3 ·
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3

Undergrad Complex numbers: don't understand graph of 1/z

  • james5
  • · Replies 4 ·
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4

Undergrad Proof that Re^(jθ) = R(cos θ + j sin θ)

  • lazypast
  • · Replies 15 ·
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15

Graduate Why do Julia sets have mirror symmetry?

  • chaoseverlasting
  • · Replies 1 ·
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1

Graduate What is the Relationship Between Metrics and Topology?

  • JasonRox
  • · Replies 10 ·
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10

Undergrad Conjugate of cos(x) using Euler's formula

  • Brewer
  • · Replies 5 ·
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5

Graduate Find the proof with supremum for bounded and disjoint sets

  • MathematicalPhysicist
  • · Replies 11 ·
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11

Undergrad What is the confusion surrounding complex numbers and their representation?

  • Muhammad Ali
  • · Replies 1 ·
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1

Undergrad Cube roots of a complex number

  • murshid_islam
  • · Replies 13 ·
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13

Graduate Questions on functions and supremums and infimums.

  • MathematicalPhysicist
  • · Replies 5 ·
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5

Graduate Proving Inequalities Between Infimum and Supremum in Subset Relations

  • MathematicalPhysicist
  • · Replies 3 ·
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3

Graduate Geometric Topology Vs. Algebraic Topology.

  • MathematicalPhysicist
  • · Replies 1 ·
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1

Undergrad Modulus of 2r cos x + ri sin x with unequal coefficients

  • aerosmith
  • · Replies 6 ·
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6

High School Using complex numbers in polar form on calculator?

  • meee
  • · Replies 2 ·
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2

Graduate Proving the Dirac delta composition formula

  • orion141
  • · Replies 3 ·
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3

Graduate Is Distance an Abstract Concept? A Debate on the Definition of Length

  • Werg22
  • · Replies 14 ·
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14

Graduate A world with no curves, artificially creating a circle?

  • Chaos' lil bro Order
  • · Replies 15 ·
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15

Undergrad Can there be 3 collinear points in a curve?

  • Skhandelwal
  • · Replies 25 ·
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25

Graduate Where to learn about toruses and n-balls for algebraic topology?

  • Evilinside
  • · Replies 5 ·
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5

Undergrad How is the multiplication rule for complex numbers derived?

  • pivoxa15
  • · Replies 11 ·
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11

Graduate What does C^r mean for functions of several variables?

  • quasar987
  • · Replies 1 ·
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1

Undergrad If you can't find a number between 0.999... and 1, are they the same?

  • BSMSMSTMSPHD
  • · Replies 60 ·
3
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60

Undergrad Can All Functions Be Plotted on a Complex Plane?

  • scott_alexsk
  • · Replies 1 ·
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1

Undergrad Complex Exponential: Why is e Used?

  • Repetit
  • · Replies 2 ·
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2

Graduate Elementary Real and Complex Analysis

  • Pseudo Statistic
  • · Replies 6 ·
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6

Graduate Residue of z/cos(z) at zeros of cos(z)

  • pivoxa15
  • · Replies 15 ·
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15

Graduate Why are topology and sigma-algebras defined in a similar way?

  • jordanl122
  • · Replies 2 ·
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2

Graduate What is

  • Dragonfall
  • · Replies 5 ·
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5

Graduate Why Are Only Constant Functions Continuous in Concrete Topology?

  • LeonhardEuler
  • · Replies 18 ·
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18

Undergrad Image of |z-1| ≤ 1 under w = 1/z in complex plane

  • simick1712
  • · Replies 4 ·
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4

Undergrad Complex number exponential subtraction

  • Exulus
  • · Replies 4 ·
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4

Graduate What is the Branch of Mathematics that Maps Entire Sub-Disciplines?

  • Lacy33
  • · Replies 4 ·
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4

Graduate Proving Noncompactness of Unit Ball in Infinite-Dimensional Banach Space

  • dextercioby
  • · Replies 2 ·
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2

Graduate Are complex numbers truly needed in quantum physics or just useful math?

  • Dense
  • · Replies 11 ·
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11

Graduate Are vertical and horizontal tori topologically equivalent?

  • DaveC426913
  • · Replies 25 ·
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25

Undergrad Bounded sequence as convergent

  • electronic engineer
  • · Replies 7 ·
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7

Graduate What is the definition of a topological space?

  • JasonRox
  • · Replies 8 ·
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8

High School What is topology?

  • En_lizard
  • · Replies 5 ·
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5

Undergrad Points in 2- and 3-dimensional space

  • symplectic_manifold
  • · Replies 4 ·
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4

Undergrad Why Does the Equation 1 = -1 Seem Correct?

  • sparkster
  • · Replies 3 ·
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3

Undergrad Good articles about complex numbers and complex envelopes

  • dervast
  • · Replies 2 ·
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2

Graduate Why is the Hilbert cube called a cube?

  • Cincinnatus
  • · Replies 3 ·
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3

Graduate A conjecture about the roots of real functions

  • eljose
  • · Replies 6 ·
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6

Undergrad What do u need to learn topology?

  • michealsmith
  • · Replies 4 ·
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4

Graduate What is the equivalence of definitions for completely regular spaces?

  • Cincinnatus
  • · Replies 2 ·
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2

Graduate Visualizing topological spaces

  • Cincinnatus
  • · Replies 5 ·
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5

Undergrad 0.999 =1 is LUB or exactly the same

  • Algorithm
  • · Replies 4 ·
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4

Undergrad Resources for learning complex numbers and De Moivre's theorem

  • shaiqbashir
  • · Replies 1 ·
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1

Graduate Complex Plane Dimension Number

  • Terry Giblin
  • · Replies 2 ·
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2

Graduate How can complex analysis be applied to Einstein's theory of relativity?

  • Tom Piper
  • · Replies 14 ·
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14

Graduate A question of roots of riemann function

  • eljose
  • · Replies 4 ·
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4

Undergrad Importance of Complex Analysis

  • heman
  • · Replies 25 ·
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25

Graduate Weierstrass approach to analysis

  • MathematicalPhysicist
  • · Replies 15 ·
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15

Graduate Explaining topology to non-mathematicians

  • octol
  • · Replies 44 ·
2
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44

Graduate How Many Roots Exist for Complex Numbers Raised to Irrational Powers?

  • cjellison
  • · Replies 2 ·
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2

Undergrad Trig chart for the complex plane

  • yourdadonapogostick
  • · Replies 22 ·
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22

Graduate Why is (algebraic) topology important?

  • octol
  • · Replies 3 ·
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3

Graduate Find a root for this expression:

  • MaxwellPhill
  • · Replies 3 ·
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3

Graduate Laurent series of the function f(z)=1/z^2 for |z-a|>|a|

  • heman
  • · Replies 7 ·
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7

Undergrad Calculate sin and cos using complex numbers

  • TomMe
  • · Replies 12 ·
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12

Graduate Complex numbers and modulus problem

  • TomMe
  • · Replies 7 ·
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7

Undergrad What are Möbius Transformations and What are Their Applications?

  • mprm86
  • · Replies 1 ·
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1

Undergrad How to Express a Complex Number in the Form of I-Tan(kA)?

  • floped perfect
  • · Replies 3 ·
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3

Graduate No Complex Analysis Equation z^4 + z + 5 = 0

  • heman
  • · Replies 13 ·
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13

Graduate Van Kampen's theorem and fundamental groups

  • sparkster
  • · Replies 7 ·
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7

Graduate What values of z in the complex plane make the series absolutely convergent?

  • heman
  • · Replies 4 ·
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4

Graduate Why is i^i equal to a real number?

  • Max cohen
  • · Replies 19 ·
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19

Graduate Uniform Metric vs Box Topology

  • joeboo
  • · Replies 2 ·
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2

Graduate Can Complex Analysis Solve x^{sin(y)}=y^{cos(x)}?

  • saltydog
  • · Replies 11 ·
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11

Graduate What is the definition of 'space'?

  • quasar987
  • · Replies 4 ·
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4

Graduate Compact sets and homeomorphisms

  • Gunni
  • · Replies 24 ·
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24

High School Understanding Imaginary Roots in Complex Numbers

  • abia ubong
  • · Replies 11 ·
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11

Undergrad Conformal mapping in Complex Analysis

  • rhia
  • · Replies 5 ·
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5

Undergrad Complex numbers and coordinates

  • BobG
  • · Replies 5 ·
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5

Undergrad Flaw in complex number square root reasoning

  • quasar987
  • · Replies 12 ·
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12

Graduate What is the basis for the inner product of functions?

  • sid_galt
  • · Replies 2 ·
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2

High School How to solve x^5 = x

  • Exulus
  • · Replies 9 ·
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9

Graduate Relative Boundaries in General Topology

  • quantumdude
  • · Replies 2 ·
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2

Graduate Can You Create a Bijective Function from the Reals to the Interval [0,1]?

  • gravenewworld
  • · Replies 1 ·
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1

Undergrad (x)=max{f(x),g(x)} continuous functions

  • QUBStudent
  • · Replies 4 ·
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4

Graduate What is complex analysis and what are its applications?

  • Gza
  • · Replies 6 ·
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6

Undergrad What is the definition of distance between a point and a set of points?

  • kakarukeys
  • · Replies 4 ·
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4

Graduate Contour Integration: Find Out Non-Removable Singularities?

  • Manchot
  • · Replies 2 ·
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2

Graduate Solving Ln(-1) with Euler's Equation

  • T@P
  • · Replies 12 ·
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12

Graduate Has the Poincaré Conjecture Been Proven? A Review of the Proposed Proof

  • Icebreaker
  • · Replies 13 ·
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13

Undergrad Sequence of rationals that converge to irrational

  • tonebone10
  • · Replies 10 ·
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10

Graduate Why are ℂ and ℝ² considered interchangeable if they have different structures?

  • cepheid
  • · Replies 4 ·
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4

Undergrad Is .999' Equal to 1? A Proof Using Reductio Ad Absurdum

  • Pyrovus
  • · Replies 13 ·
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13

Undergrad Is the Function f(x) Continuous at x=0 Given Its Definition and Behavior?

  • kidia
  • · Replies 1 ·
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1

Graduate Accumulation/densification points.

  • Galileo
  • · Replies 3 ·
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3

Graduate How can I express the coordinates of a pentagram in the complex plane using Phi?

  • arcnets
  • · Replies 6 ·
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6

Graduate Mean ergodic theorem von Neumann

  • trosten
  • · Replies 1 ·
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1