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 What are the optimal constants for the Sobolev inequalities in 3D?

  • Gerenuk
  • · Replies 1 ·
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1

Undergrad Representing complex number as a vector.

  • dE_logics
  • · Replies 6 ·
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6

Graduate Complex Exponential: What is e^jw∞?

  • tommyhakinen
  • · Replies 1 ·
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1

Graduate Unbounded and continuous almost everywhere

  • Ja4Coltrane
  • · Replies 5 ·
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5

Graduate What is the best method for plotting complex inequalities on the complex plane?

  • username12345
  • · Replies 13 ·
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13

Graduate What does the notation f|A mean?

  • pellman
  • · Replies 2 ·
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2

Graduate Open subspace of a compact space topological space

  • de_brook
  • · Replies 1 ·
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Graduate What happens to the intersection of subsets when the class is empty?

  • samkolb
  • · Replies 2 ·
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2

Graduate What is the meaning of equivalence classes in complex projective space?

  • Thorn
  • · Replies 3 ·
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3

Graduate Solving z*exp(z)=a: Proving Infinitely Many Roots

  • bndnchrs
  • · Replies 2 ·
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2

Undergrad Proving the Intersection of Open Sets is Open

  • enricfemi
  • · Replies 12 ·
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12

Graduate Solving Complex Equations: Does f(z) = 0 imply [f(z)]* = 0?

  • praharmitra
  • · Replies 5 ·
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5

Graduate What is the proof of the theorem on limit points in topology?

  • Sculptured
  • · Replies 16 ·
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16

Undergrad What is the definition of supremum and how does it relate to set A?

  • lukaszh
  • · Replies 6 ·
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6

High School What are Real and Imaginary Numbers and How Do They Relate to Each Other?

  • matt_crouch
  • · Replies 7 ·
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7

Graduate Why is \(\theta = n(\tan^{-1}(\frac{b}{a}))\) in complex exponentials?

  • Gregg
  • · Replies 1 ·
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1

Graduate Is Pure Mathematics a Waste of Time?

  • khemix
  • · Replies 33 ·
2
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33

Graduate Infinitely Many Turning Points: A Study of the Functions Re(t^i) and Im(t^i)

  • ben297
  • · Replies 1 ·
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1

High School A small problem with complex conjugations

  • Parnpuu
  • · Replies 2 ·
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2

Graduate Can a smooth function be constant on [a,b] but not everywhere?

  • csprof2000
  • · Replies 11 ·
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11

Undergrad Proof of the Intermediate Value Theorem?

  • jgens
  • · Replies 15 ·
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15

Undergrad Ready for Complex Analysis Course: MAA 4402

  • ibensous
  • · Replies 8 ·
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8

Graduate If f is entire with f(z) = f(z + 2π) = f(z + 2πi), is f constant?

  • alvielwj
  • · Replies 5 ·
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5

Graduate Is this integral a Lebesgue integral and what defines one?

  • mooberrymarz
  • · Replies 15 ·
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15

Graduate Heine-Borel theorem inequality in Rudin's Theorem 2.41

  • samspotting
  • · Replies 5 ·
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5

Graduate Can complex valued functions be written without using x+iy notation?

  • Heirot
  • · Replies 5 ·
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5

Graduate What constitutes a quotient map?

  • jhicks
  • · Replies 6 ·
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6

Graduate Prove Euler Identity without using Euler Formula

  • maze
  • · Replies 36 ·
2
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36

High School How Do Complex Number Multiplication Rules Differ from Real Number Algebra?

  • alpha01
  • · Replies 11 ·
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11

Undergrad Limit point definition: does every open interval need infinite sequence points?

  • JG89
  • · Replies 4 ·
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4

Graduate I'm going to prove every single theorem in topology

  • mathboy
  • · Replies 47 ·
2
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47

Graduate Nested sequences of rational intervals

  • JG89
  • · Replies 2 ·
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2

Graduate Why does exp(iφ) relate exponential and cosine functions?

  • Gerenuk
  • · Replies 11 ·
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11

Graduate What is a(m) in the definition of Cauchy sequences?

  • garyljc
  • · Replies 7 ·
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7

Graduate A physical meaning to complex integration

  • n0_3sc
  • · Replies 8 ·
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8

High School Understanding Complex Numbers: Squaring and Simplifying

  • Master J
  • · Replies 2 ·
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2

Undergrad Applying Cauchy's theorem formula on the complex plane

  • chota
  • · Replies 1 ·
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1

Graduate Distance function from x to the Cantor set

  • Dragonfall
  • · Replies 6 ·
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6

Graduate Question regarding the definition of the complex fourier series

  • Narcol2000
  • · Replies 2 ·
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2

Graduate What if one of Dedekind cut's properties were omitted?

  • Ronn
  • · Replies 1 ·
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1

Undergrad Real Numbers: Show Base b Analogy Properties

  • Diffy
  • · Replies 1 ·
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1

Graduate Complex Variable Methods Lecture Notes

  • iopmar06
  • · Replies 4 ·
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4

Graduate How to fit a complex equation?

  • bitele
  • · Replies 3 ·
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3

Graduate Proving $\Im (\ln(-|x|))=\pi$ for All Reals

  • epkid08
  • · Replies 2 ·
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2

Graduate Is Brushing Up on Analysis Enough for a Graduate Course in Mathematical Finance?

  • esahione
  • · Replies 4 ·
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4

Undergrad What Happens to sin(i) for Complex i?

  • hadi amiri 4
  • · Replies 57 ·
2
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57

Graduate Simple Connectedness of [0,1]^k

  • quasar987
  • · Replies 3 ·
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3

Graduate Visualizing Point at Infinity - Euclidean Plane

  • Gear300
  • · Replies 3 ·
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3

Graduate Quotient of l_1(I) by c_0(I) and tensor products

  • olliemath
  • · Replies 1 ·
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1

Graduate Complex conjugate an independent variable?

  • Chen
  • · Replies 8 ·
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8

Graduate Is regularity preserved in subsets of regular spaces?

  • ice109
  • · Replies 3 ·
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3

Undergrad How are the complex plane and real plane graphically related?

  • chaoseverlasting
  • · Replies 9 ·
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9

Graduate Is R with the cofinite topology path connected?

  • ice109
  • · Replies 4 ·
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4

Graduate Algebraic geometry/topology - ramification - sheaf cohomology

  • bb16
  • · Replies 3 ·
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3

Graduate Euclidean Neighbourhoods are always open sets

  • lantern
  • · Replies 7 ·
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7

Undergrad Liberty League International Complex Numbers

  • Liberty Leagu
  • · Replies 7 ·
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7

Undergrad Raising a complex number to the nth power

  • magda3227
  • · Replies 7 ·
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7

Graduate Visualizing intersecting multidimensional objects.

  • Keys
  • · Replies 3 ·
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3

Undergrad How to solve z^3 = i and other equations with complex numbers

  • lostinphys
  • · Replies 4 ·
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4

Graduate What is wrong with the following proof

  • snipez90
  • · Replies 3 ·
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3

Undergrad Why does i*j*k=-1 in quaternion algebra?

  • Adder_Noir
  • · Replies 14 ·
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14

High School We usually represent sqrt(-1) as i

  • svigneshkumars
  • · Replies 17 ·
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17

Undergrad Finding Real and Imaginary Parts of Complex Numbers

  • magda3227
  • · Replies 3 ·
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3

Undergrad What sets of points have well-defined area or volume?

  • Werg22
  • · Replies 2 ·
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2

Graduate Why is 1+i = root 2e^(pi/4+2pi k) true?

  • The_ArtofScience
  • · Replies 3 ·
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3

Graduate Can the image of f(x)=\cos x + i \sin x be proven to be the unit circle?

  • CrumpledPaper
  • · Replies 17 ·
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17

Graduate Complex Analysis: Proving Bounds for |e^z-1|

  • the1ceman
  • · Replies 3 ·
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3

Undergrad Complex Exponent Rules and Misconceptions

  • Dark Fire
  • · Replies 9 ·
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9

Graduate What are some applications of the concept of complex infinity?

  • Beer w/Straw
  • · Replies 43 ·
2
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43

Graduate Inequality in Körner's problem 1.16 about continuity in ℚ

  • mlearner
  • · Replies 7 ·
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7

Undergrad What is the multiplicity of a pole in complex analysis?

  • Icosahedron
  • · Replies 8 ·
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8

Graduate Evaluating Complex Integral: Over |z|=4 Region

  • fudgenstuff
  • · Replies 5 ·
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5

Graduate Exponential law and complex numbers

  • Positronized
  • · Replies 3 ·
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3

Graduate Is f(x) as the 100th Decimal Place Digit a Function?

  • (_8^(1)
  • · Replies 8 ·
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8

Graduate An infinite amount of permutations,

  • daniel_i_l
  • · Replies 2 ·
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2

Graduate What is the proof for the Riemann Series Theorem?

  • daniel_i_l
  • · Replies 5 ·
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5

Graduate What Did Hermann Weyl Mean by We are Left with Our Symbols?

  • pivoxa15
  • · Replies 8 ·
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8

Undergrad Applications of Complex Variables

  • DaVinci
  • · Replies 8 ·
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8

Graduate Topology Questions: Isham's Modern Differential Geometry for Physicists

  • UJS
  • · Replies 3 ·
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3

Graduate Algebraic Manipulation of Euler's Identity Leads to a Strange Result

  • amolv06
  • · Replies 3 ·
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3

High School Questions about imaginary number and root of 4

  • Shing
  • · Replies 10 ·
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10

Graduate Compact operators on infinite dimensional Banach spaces are never invertible

  • quasar987
  • · Replies 6 ·
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6

Graduate Covering Sphere w/ Disks: Min Required Radius k

  • Ynaught?
  • · Replies 5 ·
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5

Graduate Examples of sets that are both open and closed, or neither

  • Ka Yan
  • · Replies 2 ·
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2

Graduate Is continuity of the derivative sufficient for analyticity?

  • ultimateceej
  • · Replies 2 ·
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2

Graduate Does Every Topology Have a Minimal Subset Basis?

  • mathboy
  • · Replies 2 ·
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2

Graduate How did separable spaces get their name?

  • quasar987
  • · Replies 1 ·
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1

Graduate Conflicting statements from two topology textbooks

  • mathboy
  • · Replies 2 ·
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2

Graduate Typo in Real Analysis Study Page: Absolute Value of x for x<0?

  • starkind
  • · Replies 3 ·
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3

Graduate How many fixed points on a circle S/Z2?

  • Living_Dog
  • · Replies 6 ·
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6

Graduate Is there a relation between coarseness and metrizability?

  • quasar987
  • · Replies 1 ·
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1

Graduate Compactness of the unit ball in infinite dimension

  • quasar987
  • · Replies 12 ·
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12

Graduate Hausdorffness of the product topology

  • quasar987
  • · Replies 4 ·
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4

Undergrad Need hands to the Rational Set

  • Ka Yan
  • · Replies 9 ·
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9

Graduate Difference between perfect and complete sets, and how to verify compactness

  • Ka Yan
  • · Replies 2 ·
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2

Graduate Supplementary books for real analysis beyond Körner

  • MrGandalf
  • · Replies 7 ·
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7

Graduate Why doesn't the gamma function integral diverge for negative non-integer z?

  • vcdfrexzaswq
  • · Replies 3 ·
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3

Graduate Can Two-Moves Separate Components of a Link in Knot Theory?

  • de1irious
  • · Replies 2 ·
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2

Undergrad How to map intervals of Real line

  • Diffy
  • · Replies 5 ·
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5

Graduate Solving of the Poincare' Conjecture

  • vincentm
  • · Replies 1 ·
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1