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 Solving Polynomials with Complex Coefficients

  • ||spoon||
  • · Replies 4 ·
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4

Graduate How do i find k in the banach fixed point theorem

  • sara_87
  • · Replies 5 ·
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5

Graduate What Does the Banach Fixed Point Theorem Mean?

  • sara_87
  • · Replies 3 ·
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3

Undergrad Why does sqrt(-1) = (-1)^(1/2) = ... = 1 look correct?

  • Diffy
  • · Replies 6 ·
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6

Graduate Can topology be taught before rigorous calculus?

  • rudinreader
  • · Replies 3 ·
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3

Graduate Are All Filters Both Finer and Coarser Than Themselves?

  • Saketh
  • · Replies 1 ·
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1

Graduate Identify an advanced point-set topology textbook from 1966-1975

  • mathboy
  • · Replies 4 ·
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4

Graduate Can 0^(ia) Have a Definite Solution for Positive Real a?

  • intangible
  • · Replies 2 ·
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2

Graduate Reading multiple books simultaneously on the same subject

  • mathboy
  • · Replies 2 ·
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2

Graduate How Can I Prove These Topology Statements?

  • rolylane
  • · Replies 5 ·
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5

Undergrad Straight lines and complex numbers

  • saiaspire
  • · Replies 2 ·
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2

Graduate Banach Spaces vs. Closed Spaces: What's the Difference?

  • hooker27
  • · Replies 6 ·
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6

Undergrad Recommend a good book on complex analysis?

  • wildman
  • · Replies 11 ·
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11

Graduate Betti numbers and euler characterstic?

  • Coolphreak
  • · Replies 1 ·
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1

Graduate Rigorization of analysis and calculus in the 19th century and since

  • titaniumx3
  • · Replies 5 ·
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5

Graduate Calculating Homology Groups of RP(2)

  • Sephi
  • · Replies 2 ·
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2

Graduate Limit in closure, topology stuff

  • jostpuur
  • · Replies 13 ·
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13

Graduate Topology Question (Normal Spaces)

  • BSMSMSTMSPHD
  • · Replies 1 ·
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1

Graduate Is this proof that C is compact in X when C is compact in F correct?

  • shapiro478
  • · Replies 12 ·
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12

Undergrad So the question would be:What is the difference between absolute value and norm?

  • lampshade
  • · Replies 9 ·
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9

Graduate Is U-A Open and A-U Closed in Topological Spaces?

  • MathematicalPhysicist
  • · Replies 2 ·
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2

Graduate Is every component of a product of Hausdorff spaces also Hausdorff?

  • mathboy
  • · Replies 9 ·
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9

Graduate How Do Riemann and Lebesgue Integrals Compare in Integration Theory?

  • quasar987
  • · Replies 39 ·
2
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39

Graduate What is the dimension of a topological space?

  • princeton118
  • · Replies 7 ·
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7

Graduate Using Liouville's Theorem to Show f is Constant

  • smoothman
  • · Replies 2 ·
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2

Graduate Proving Equality of Subspace Topologies: A Topological Lemma Approach

  • MathematicalPhysicist
  • · Replies 6 ·
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6

Graduate Is a Function with Two Non-Commutative Periods Necessarily Constant?

  • Office_Shredder
  • · Replies 8 ·
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8

Graduate Unique Partition of Evenly Covered Sets in Algebraic Topology

  • JasonRox
  • · Replies 8 ·
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8

Undergrad Why are there two square roots of -1 in complex numbers?

  • Zorodius
  • · Replies 11 ·
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11

Graduate Surjectivity of Induced Homomorphism in Algebraic Topology

  • JasonRox
  • · Replies 7 ·
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7

Graduate Find a function f(z) such that f(f(z)) = exp(z)

  • Count Iblis
  • · Replies 20 ·
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20

Graduate What does S^1 X S^1 really mean?

  • pivoxa15
  • · Replies 2 ·
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2

Graduate What is compactness and how does it relate to uniform continuity?

  • futurebird
  • · Replies 14 ·
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14

Graduate Non planar simplicial homology?

  • Coolphreak
  • · Replies 3 ·
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3

Undergrad Triangle Inequality Proof theorem

  • Howers
  • · Replies 2 ·
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2

Graduate What is the motivation behind homology?

  • pivoxa15
  • · Replies 4 ·
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4

Graduate Complex powers/logarithmic spirals

  • hoodwink
  • · Replies 2 ·
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2

Graduate Queer questions about topology

  • navigator
  • · Replies 5 ·
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5

Graduate Why is the infinite Cartesian product of [0,1] with itself not countably based?

  • Extropy
  • · Replies 7 ·
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7

Undergrad Uses of Topology: Learn What It Can Do

  • 111111
  • · Replies 2 ·
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2

Graduate Contraction of a Line Segment Using Average Point

  • matteo16
  • · Replies 4 ·
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4

Graduate Is Multi-Valued Functions a Misnomer?

  • Gib Z
  • · Replies 11 ·
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11

Graduate Is it true that ||z| - |w|| \leq |z + w| ?

  • smoothman
  • · Replies 1 ·
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1

Graduate Proving open and closed sets in the complex plane

  • heyo12
  • · Replies 2 ·
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2

Graduate Sequence that has a subsequence that converges towards any value in R

  • Werg22
  • · Replies 5 ·
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5

Graduate Countable But Not Second Countable Topological Space

  • Nolen Ryba
  • · Replies 3 ·
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3

Graduate Why can we assume 0.5|x - 4| < ε in epsilon-delta proofs?

  • bjgawp
  • · Replies 4 ·
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4

Graduate In the derivation of a cycloid - problem in Stewart

  • tronter
  • · Replies 4 ·
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4

Graduate Does flux through a closed surface depend on topology?

  • Coolphreak
  • · Replies 3 ·
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3

Graduate Where does this inequality come from?

  • michaelxavier
  • · Replies 2 ·
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2

Graduate Real Analysis- least upper bound and convergence

  • Scousergirl
  • · Replies 4 ·
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4

Graduate How supposed I imagine the following equations?

  • tomcenjerrym
  • · Replies 1 ·
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1

Graduate Why is identification topology called quotient topology?

  • navigator
  • · Replies 3 ·
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3

High School Why are real and imaginary numbers perpendicular axes in the complex plane?

  • JPC
  • · Replies 10 ·
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10

Undergrad What is the difference between norm and modulus?

  • cks
  • · Replies 6 ·
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6

Graduate What is the Dedekind section definition of a lower bound?

  • ice109
  • · Replies 5 ·
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5

Graduate Why does applying Dedekind cuts to the reals give reals?

  • ice109
  • · Replies 1 ·
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1

Graduate Is every subspace of a connected space connected?

  • quantum123
  • · Replies 12 ·
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12

Graduate An set without limit points - Necessarily closed?

  • Extropy
  • · Replies 15 ·
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15

Graduate Does dividing a function by a smooth function result in a smooth function?

  • tronter
  • · Replies 1 ·
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1

Undergrad Trig functions on complex numbers?

  • davee123
  • · Replies 3 ·
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3

High School What's the deal with imaginary numbers?

  • LHarriger
  • · Replies 9 ·
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9

Graduate Computing Relative Homology Groups from a Given Map

  • bham10246
  • · Replies 7 ·
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7

Graduate Proving Triviality of pi_1(S^n;e) in Algebraic Topology

  • bham10246
  • · Replies 7 ·
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7

Undergrad Is 2 pi i equal to 0, contradicting the fact that pi and i cannot equal 0?

  • nicktacik
  • · Replies 5 ·
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5

Undergrad Cancelling Confusion with Complex Numbers and De Moivre's Theorem

  • Trail_Builder
  • · Replies 2 ·
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2

Graduate Computing the homology of R^3 - S^1

  • bham10246
  • · Replies 5 ·
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5

Graduate Riemann surface, elliptic curves

  • Ratzinger
  • · Replies 6 ·
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6

Graduate How is the Void Open in the Topology of R^n?

  • quasar987
  • · Replies 6 ·
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6

Graduate Is a continuous bijection from ℝ³ to itself always a homeomorphism?

  • Xian'an Jin
  • · Replies 12 ·
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12

Undergrad What is 'cluster point' in french?

  • quasar987
  • · Replies 10 ·
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10

Undergrad What is the Formula for Multiplying Complex Numbers in Polar Form?

  • Joza
  • · Replies 5 ·
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5

Graduate Proof: Complex Number w^2+(5/w)-2=0 is Purely Imaginary

  • ahoy hoy
  • · Replies 2 ·
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2

Graduate Worldsheet and complex analysis stuff

  • nrqed
  • · Replies 13 ·
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13

Undergrad Converting Complex Numbers to Trigonometric Identities

  • Joza
  • · Replies 8 ·
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8

Graduate What is the Definition of a Conic in Complex Projective 2 Space?

  • Diophantus
  • · Replies 2 ·
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2

Graduate Graphing Euler Relationship as exponential spiral

  • KeyLime
  • · Replies 5 ·
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5

Graduate Prove Injectivity of x^x Function?

  • Izzhov
  • · Replies 32 ·
2
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32

Undergrad Calculating the Imaginary Part of (1-2i)^2-i

  • Anood
  • · Replies 1 ·
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1

Undergrad Complex Numbers: Solving 2^(8n)exp^(2niπ)=2^(8n)

  • craig100
  • · Replies 5 ·
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5

High School Solving Complex Numbers: How Does 1 + i Equal √2?

  • craig100
  • · Replies 8 ·
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8

Graduate Fully Developed Areas in Mathematics

  • RJ Emery
  • · Replies 4 ·
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4

Graduate + infinity and - infinity join ?

  • JPC
  • · Replies 4 ·
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4

Graduate Why does [f]*[g] = [f*g] for path-homotopy equivalence classes?

  • JasonRox
  • · Replies 11 ·
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11

Graduate Can the reals be characterized by topological properties?

  • DeadWolfe
  • · Replies 3 ·
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3

Undergrad Why is the square root of i equal to exp(iπ/4)?

  • neu
  • · Replies 17 ·
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17

High School Are Infinite Points on a Straight Line Just One Point?

  • nine
  • · Replies 35 ·
2
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35

Undergrad Solving for z with Complex Numbers

  • Jeff Cook
  • · Replies 14 ·
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14

Undergrad Proof Complex Numbers: How to Prove |z1|^2/|z2|^2 = |z1/z2|^2

  • Suni
  • · Replies 2 ·
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2

Undergrad Is ln(-1) Equal to Zero?

  • alba_ei
  • · Replies 14 ·
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14

Undergrad Can sinh x = 0 and cosh z = 0 Be Solved Simultaneously?

  • En_lizard
  • · Replies 9 ·
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9

Undergrad What is the mathematical equation for calculating the arg function?

  • pyro_dragun
  • · Replies 5 ·
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5

Graduate Why not use contour integration for the Fourier transform integral

  • Swapnil
  • · Replies 2 ·
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2

Graduate Symbols for homeomorphic, isomorphic, homotopic

  • quasar987
  • · Replies 5 ·
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5

Graduate Proving Real Numbers Satisfy Inequality

  • murshid_islam
  • · Replies 10 ·
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10

Undergrad What are extended plane and extended space?

  • *best&sweetest*
  • · Replies 1 ·
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1

Undergrad What is a pathological function and how can it be constructed?

  • Swapnil
  • · Replies 12 ·
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12

Undergrad May be a stupid question, but bothering me for long time

  • christinaz
  • · Replies 16 ·
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16

Graduate Why Do Different Math Textbooks Use Varying Definitions and Notations?

  • Tom1992
  • · Replies 6 ·
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6

Undergrad Having trouble with complex quadratic equations

  • Jeff Cook
  • · Replies 5 ·
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5