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.

Threads

Undergrad Using Intermediate Value Theorem to prove # of polynomial roots

  • KingNothing
  • · Replies 1 ·
Replies
1

Graduate What are the conditions for non-integer exponents to be single valued?

  • Black Integra
  • · Replies 1 ·
Replies
1

Graduate Looking for reading suggestions

  • Minimonster
  • · Replies 2 ·
Replies
2

Undergrad What behind the idea of representing real numbers as points ?

  • mahmoud2011
  • · Replies 6 ·
Replies
6

Graduate ALgebraic Topology Query (Hatcher) - Not Homework

  • Singularity
  • · Replies 3 ·
Replies
3

Graduate Why is (0,1) not compact in topology?

  • Newtime
  • · Replies 35 ·
2
Replies
35

Undergrad Limits of Complex exponentials

  • Sanjeev-ISE
  • · Replies 4 ·
Replies
4

Graduate Is a general sequence possible for the given data?

  • SithsNGiggles
  • · Replies 2 ·
Replies
2

Graduate Is the cantor set diffeomorphic to the fat cantor set?

  • LBloom
  • · Replies 23 ·
Replies
23

Undergrad Mathematical objects, structures and spaces

  • autodidude
  • · Replies 5 ·
Replies
5

Graduate Understanding the Implication in the Proof of a Theorem

  • MIB
  • · Replies 13 ·
Replies
13

Graduate What is the Inner Product Space for Square-Integrable Functions?

  • mekarim
  • · Replies 2 ·
Replies
2

Graduate Why the circle can't be homeomorphic to a real interval

  • camel_jockey
  • · Replies 17 ·
Replies
17

Graduate [Topology] why the words finer and coarser ?

  • nonequilibrium
  • · Replies 6 ·
Replies
6

Graduate What metric from given manifold?

  • gunnpark
  • · Replies 8 ·
Replies
8

Graduate The usual topology is the smallest topology containing the upper and lower topology

  • rlkeenan
  • · Replies 2 ·
Replies
2

Graduate How Does Cutting a Torus with a Mobius Strip Alter Its Geometry?

  • addedline8
  • · Replies 3 ·
Replies
3

Graduate Angle on abstract metric space, has sense?

  • Damidami
  • · Replies 12 ·
Replies
12

Graduate How Do We Know That Every Closed Subset of the Cantor Set Is a Retract?

  • Bacle
  • · Replies 10 ·
Replies
10

Graduate Is the Quotient Space of Identifying Rational Numbers Compact and Hausdorff?

  • felper
  • · Replies 9 ·
Replies
9

Graduate Definition of boundary operator

  • GatorPower
  • · Replies 2 ·
Replies
2

Graduate Smooth manifolds and affine varieties

  • ForMyThunder
  • · Replies 4 ·
Replies
4

Graduate Understanding Function Spaces: What Are They?

  • coverband
  • · Replies 11 ·
Replies
11

Graduate Continuous Bijection f:X->X not a Homeo.

  • Bacle
  • · Replies 9 ·
Replies
9

Graduate Can someone explain the resolution to the complex power paradox?

  • LAHLH
  • · Replies 10 ·
Replies
10

Graduate Lipschitz function and Baire Category Theorem

  • itzik26
  • · Replies 4 ·
Replies
4

Graduate Proper Function: Homeomorphism or Not?

  • Lie
  • · Replies 5 ·
Replies
5

Graduate Topology Problems for Challenging Students

  • micromass
  • · Replies 32 ·
2
Replies
32

Graduate Generalizations (from metric to topological spaces)

  • Fredrik
  • · Replies 6 ·
Replies
6

Undergrad How many square roots does a complex number have?

  • dalcde
  • · Replies 3 ·
Replies
3

Graduate Finite Supremum and Infinium Solution for Munkres Text Question 20.7

  • Fisicks
  • · Replies 2 ·
Replies
2

Graduate How does the second paragraph prove that \tau' is the same as \tau?

  • camilus
  • · Replies 2 ·
Replies
2

Graduate Verifying the metric space e = d / (1 + d)

  • pdonovan
  • · Replies 4 ·
Replies
4

Undergrad Understanding Arccos(x) for Values Outside [-1, 1]

  • Philosophaie
  • · Replies 7 ·
Replies
7

Graduate Jordan-Brouwer Separation Theorem and Invariance of Domain

  • Anonymous217
  • · Replies 10 ·
Replies
10

Graduate Describing All covering Spaces of a Product Space

  • Bacle
  • · Replies 5 ·
Replies
5

Graduate CP^2 , and CP^2 -bar, are not diffeomorphic.

  • WWGD
  • · Replies 10 ·
Replies
10

Undergrad Basic knowledge about real analysis

  • sumit_kumar
  • · Replies 2 ·
Replies
2

Graduate Homemorphism between the set of circles with rational points and rectangles

  • praveen97uma
  • · Replies 2 ·
Replies
2

Graduate Cartesian product of separable metric spaces

  • Andeweld
  • · Replies 2 ·
Replies
2

Undergrad Intro to Topology Recommended Texts

  • STEM2012
  • · Replies 7 ·
Replies
7

Graduate Understanding Complex Func., Laplace Transforms & Cauchy Riemann

  • phiby
  • · Replies 3 ·
Replies
3

Graduate Local Continuity and Restriction

  • Bacle
  • · Replies 4 ·
Replies
4

Graduate A convergent sequence of reals

  • Dr. Seafood
  • · Replies 7 ·
Replies
7

Graduate Should I take general topology or complex analysis?

  • henryN7
  • · Replies 2 ·
Replies
2

Graduate Unleashing a Cyber Attack: The Dangers of Corrupting the Internet

  • Fredrik
  • · Replies 9 ·
Replies
9

Undergrad Complex number problem, could the problem be wrong?

  • mariush
  • · Replies 7 ·
Replies
7

Graduate Definitions of topology and analysis

  • Fredrik
  • · Replies 7 ·
Replies
7

Graduate Foliation of 4-dimensional connected Hausdorff orientable paracompact manifold

  • ivl
  • · Replies 13 ·
Replies
13

Graduate Cauchy Reimann & Complex functions

  • phiby
  • · Replies 2 ·
Replies
2

Graduate How can we find the true solution for cosh x = tanh x?

  • dimension10
  • · Replies 12 ·
Replies
12

Graduate How important is topology for modern mathematics?

  • kramer733
  • · Replies 9 ·
Replies
9

Graduate Polya and Szego Problems in Analysis?

  • ArcanaNoir
  • · Replies 1 ·
Replies
1

Graduate Does an Homeomorphism Preserve Boundary Correspondence in Topological Spaces?

  • aleazk
  • · Replies 9 ·
Replies
9

Graduate Question about the Banach–Tarski paradox.

  • cragar
  • · Replies 7 ·
Replies
7

Graduate Analytic Function (3+x-iy)^7 in Domain [z]<2?

  • tibphysic
  • · Replies 1 ·
Replies
1

Graduate Theorem 1.21 Rudin. Obviously wrong stated, right?

  • saim_
  • · Replies 3 ·
Replies
3

Undergrad How do you take this complex conjugate?

  • AxiomOfChoice
  • · Replies 4 ·
Replies
4

Graduate Answer for Munkres Topology Problem 17.18 - Share Your Solution!

  • Fisicks
  • · Replies 2 ·
Replies
2

High School Reviewing How to Find Complex Roots: e.g. x3= 8

  • BloodyFrozen
  • · Replies 4 ·
Replies
4

Graduate Closed Subsets and Limits of Sequences: A Topology Book Example

  • Fredrik
  • · Replies 5 ·
Replies
5

Undergrad Can one excel in higher level math courses without studying real analysis?

  • autre
  • · Replies 3 ·
Replies
3

Graduate How Does the Fubini-Study Metric Compare to the Standard Metric on the 2-Sphere?

  • lavinia
  • · Replies 6 ·
Replies
6

Graduate Convergent subsequences in compact spaces

  • redbowlover
  • · Replies 11 ·
Replies
11

Graduate Topological and neighbourhood bases

  • Rasalhague
  • · Replies 5 ·
Replies
5

Graduate Product of compact sets compact in box topology?

  • spicychicken
  • · Replies 3 ·
Replies
3

Graduate Open and closed sets in metric spaces

  • Dr. Seafood
  • · Replies 2 ·
Replies
2

Graduate Proof that a function is of exponential order

  • awelex
  • · Replies 5 ·
Replies
5

Graduate Understanding Homotopies and Degree Invariance in Topology

  • jgens
  • · Replies 2 ·
Replies
2

Graduate Is the Function F(x, y) Continuous at All Points?

  • tomboi03
  • · Replies 3 ·
Replies
3

Undergrad What does All but finitely many n mean?

  • kntsy
  • · Replies 8 ·
Replies
8

Undergrad Why does the 'i' disappear in the simplification of a complex number sum?

  • RoughRoad
  • · Replies 4 ·
Replies
4

Graduate Examples of infinite/arbitrary unions of closed sets that remain closed.

  • wisvuze
  • · Replies 3 ·
Replies
3

Graduate Topology question → What geometric figure?

  • ukumari
  • · Replies 3 ·
Replies
3

Graduate Is every Closed set a complete space?

  • alemsalem
  • · Replies 6 ·
Replies
6

Graduate What Is the Real Part of x Divided by the Factorial of -1?

  • elegysix
  • · Replies 6 ·
Replies
6

Graduate A compact, B closed Disjoint subsets of Metric Space then d(A,B)=0

  • Bacle
  • · Replies 4 ·
Replies
4

Graduate Topology Q: Show f is Continuous in X with d and A

  • mbarby
  • · Replies 3 ·
Replies
3

Graduate Convergence of a sequence of points on a manifold

  • yifli
  • · Replies 3 ·
Replies
3

Graduate Bounding the Diameter of Union of Two Sets in a Metric Space

  • nirajkadiyan6
  • · Replies 7 ·
Replies
7

Graduate What combinations satisfy this complex exponentiation property?

  • bruno67
  • · Replies 3 ·
Replies
3

Undergrad Complex Number Graph : x^5 = 1

  • jlpmghrs
  • · Replies 5 ·
Replies
5

Graduate Homeomorphisms Send Bdries to Bdries

  • Bacle
  • · Replies 4 ·
Replies
4

Graduate Accumulation Points in [0,1]: Understanding the Boundaries

  • mbarby
  • · Replies 9 ·
Replies
9

Graduate What happens when we rise a number to the power of i ?

  • momentweaver
  • · Replies 6 ·
Replies
6

Graduate Showing Dense G_δ-Subspace of Baire Space is a Baire Space

  • Lie
  • · Replies 2 ·
Replies
2

Graduate Open Sets in R^n: Show Dot Product Is Open

  • seydunas
  • · Replies 6 ·
Replies
6

Graduate The meaning of different in Munkres' Topology

  • madsmh
  • · Replies 2 ·
Replies
2

Graduate Complex Analysis/Topology Proof Help

  • MurraySt
  • · Replies 4 ·
Replies
4

Graduate Topolgy with Thoughtspacezero (youtube)(error?)

  • Kidphysics
  • · Replies 8 ·
Replies
8

Undergrad Connection between Monotone and One-to-one Functions

  • hadron23
  • · Replies 10 ·
Replies
10

Undergrad Functional iteration and convergence

  • bbb999
  • · Replies 14 ·
Replies
14

Undergrad When does the argument of a complex number follow the sum of angles formula?

  • Snowfall
  • · Replies 4 ·
Replies
4

Graduate Proving Compactness of a Topological Group Using Subgroups and Quotient Spaces

  • Lie
  • · Replies 10 ·
Replies
10

Undergrad Learn Topology: Resources for Beginners

  • dalcde
  • · Replies 12 ·
Replies
12

Graduate Is the Riemann Zeta Function of 0 Infinity or -1/2?

  • dimension10
  • · Replies 7 ·
Replies
7

Undergrad Plotting e^(a+ix) for Beginners

  • silent_hunter
  • · Replies 7 ·
Replies
7

Graduate Open sets in R being the union of open intervals

  • wisvuze
  • · Replies 2 ·
Replies
2

Graduate How to show induced topological space

  • ismaili
  • · Replies 3 ·
Replies
3

Graduate Continuity in Half Interval Topology for x^2 Function

  • Slats18
  • · Replies 10 ·
Replies
10