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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Threads

Graduate Can Equilibrium State Determine Complex Potential?

  • binbagsss
  • · Replies 5 ·
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5

High School Finite linear combination of continuous functions is continuous?

  • docnet
  • · Replies 3 ·
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3

Undergrad Verify the completion of continuous compactly supported functions

  • psie
  • · Replies 4 ·
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4

Undergrad Fiber bundle homeomorphism with the fiber

  • cianfa72
  • · Replies 43 ·
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43

Undergrad On deriving the (inverse) Fourier transform from Fourier series

  • psie
  • · Replies 4 ·
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4

Undergrad Prove projection of a measurable set from product space is measurable

  • Lagrange fanboy
  • · Replies 3 ·
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3

High School Questions on a numberphile video

  • picketpocket826
  • · Replies 5 ·
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5

Undergrad ##SU(2, \mathbb C)## parametrization using Euler angles

  • cianfa72
  • · Replies 15 ·
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15

Undergrad Regarding Wirtinger's inequality

  • psie
  • · Replies 4 ·
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4

Undergrad ##SL(2,\mathbb R)## Lie group as manifold

  • cianfa72
  • · Replies 12 ·
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12

High School A Question Relating Sum of Angles and Breaking of the Parallel Postulate

  • walkeraj
  • · Replies 6 ·
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6

Undergrad ##1^x =2## has complex solutions?

  • Arjan82
  • · Replies 7 ·
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7

Undergrad Is the Projection Restriction to a Linear Subspace a Homeomorphism?

  • cianfa72
  • · Replies 8 ·
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8

Undergrad New Video Course on General Topology on YouTube

  • caffeinemachine
  • · Replies 2 ·
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2

Undergrad On a proof of the converse of the supporting hyperplane theorem

  • psie
  • · Replies 9 ·
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9

Undergrad ##SU(2)## homeomorphic with ##\mathbb S^3##

  • cianfa72
  • · Replies 61 ·
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61

Undergrad Bloch Analysis proof of Theorem 2.5.5 (Definition by recursion)

  • BugKingpin
  • · Replies 2 ·
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2

Undergrad How do I use the four axioms of a neighborhood to define an open set?

  • learning physics
  • · Replies 2 ·
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2

Undergrad How to define an open set using the four axioms of a neighborhood

  • learning physics
  • · Replies 2 ·
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2

Undergrad Is the Belt Trick Possible with Continuous Deformation in 3D Rotation Space?

  • cianfa72
  • · Replies 8 ·
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8

Undergrad On differentiability and Fourier coefficients (Vretblad's text)

  • psie
  • · Replies 4 ·
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4

Graduate Examples of essential singularities in complex analysis

  • LagrangeEuler
  • · Replies 6 ·
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6

Undergrad On limit of convolution of function with a summability kernel

  • psie
  • · Replies 2 ·
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2

Undergrad Fourier coefficients of convolution

  • psie
  • · Replies 1 ·
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1

Undergrad Result 2.14: outer measure and interval length in Axler

  • Math Amateur
  • · Replies 8 ·
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8

Undergrad Bounding modulus of complex logarithm times complex power function

  • psie
  • · Replies 4 ·
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4

High School Why is a circle allowed in the Poincaré conjecture if a line with endpoints isn't?

  • shiv23mj
  • · Replies 2 ·
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2

Undergrad Is a Locally One-to-One Proper Map Globally Bijective?

  • Ashley1209
  • · Replies 8 ·
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8

Undergrad On a remark regarding the Cauchy integral formula

  • psie
  • · Replies 2 ·
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2

Undergrad Continuity of Quotient of Complex Values

  • thatboi
  • · Replies 5 ·
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5

Undergrad Complex function, principal value notation

  • Hill
  • · Replies 5 ·
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5

Undergrad Infinity Numbers (Expanded P-Adic Numbers)

  • Lokalgott
  • · Replies 10 ·
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10

High School Getting from complex domain to real domain

  • jaydnul
  • · Replies 3 ·
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3

Undergrad Naming convention for "Functional Variance"?

  • quasar987
  • · Replies 7 ·
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7

Undergrad Why is f(u)e^(iω(t-u)) not L¹(ℝ×ℝ)?

  • laurabon
  • · Replies 6 ·
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6

High School Why is the set {(x,y)∈Ω×R|y=f(x)} a manifold?

  • SaschaSIGI
  • · Replies 6 ·
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6

Graduate Topology - Boundary of a ball without a point

  • physics1000
  • · Replies 5 ·
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5

Graduate Why the triangle inequality is greater than the 2 max{f(x),g(x)}

  • cbarker1
  • · Replies 1 ·
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1

Undergrad Feedback for my YouTube Videos on Real Analysis

  • caffeinemachine
  • · Replies 4 ·
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4

High School How Do Dedekind Cuts Affect Addition and Negative Numbers?

  • bhobba
  • · Replies 6 ·
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6

Undergrad Using Residues (Complex Analysis) to compute partial fractions

  • cbarker1
  • · Replies 4 ·
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4

Undergrad Is the Set of Integer Outputs of sin(x) Sequentially Compact in ℝ?

  • MidgetDwarf
  • · Replies 3 ·
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3

Graduate Even with a whimsical mathematical usage, solutions are obtained!

  • Z-10-46
  • · Replies 5 ·
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5

Undergrad Circuits or edge-disjoint unions of circuits in a connected graph

  • cianfa72
  • · Replies 1 ·
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1

Undergrad How can you represent a point by "z = x + iy" as shown here?

  • Slimy0233
  • · Replies 10 ·
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10

Undergrad Can you somehow make left handed helix into a right handed?

  • sol47739
  • · Replies 8 ·
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8

Axler's result 2.8: arranging intervals to prove countable subadditivity

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Calculate the residue of 1/Cosh(pi.z) at z = i/2 (complex analysis)

  • Old Person
  • · Replies 7 ·
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7

High School Does the waveform y = 0 have an inverse?

  • bahamagreen
  • · Replies 3 ·
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3

High School Is π+arctan(2) a complex number in the second quadrant?

  • mcastillo356
  • · Replies 7 ·
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7

High School Wolfram Alpha's Why the 2 i π n?

  • OmCheeto
  • · Replies 3 ·
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3

High School Aperiodic Tiling with a single tile shape

  • .Scott
  • · Replies 5 ·
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5

Graduate Regarding fibrations between smooth manifolds

  • aalma
  • · Replies 1 ·
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1

Undergrad Geometry of series terms of the Riemann Zeta Function

  • Swamp Thing
  • · Replies 3 ·
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3

Undergrad I need a mapping from the unit Hypercube [0,1]^n to a given simplex

  • benorin
  • · Replies 17 ·
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17

Undergrad When does a discrete subring of the reals become dense?

  • Paul Colby
  • · Replies 11 ·
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11

Checking Proof of Theorem 6.2.8 Part (ii)

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad I would like opinions of the latest draft of my note - Integration

  • benorin
  • · Replies 4 ·
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4

Undergrad Upper and Lower Darboux Sum Inequality

  • Magnetons
  • · Replies 2 ·
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2

Graduate Does Perelman's proof of the Poincaré conjecture imply the universe is a 3-sphere surface?

  • donglepuss
  • · Replies 3 ·
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3

Undergrad Original definition of Riemann Integral and Darboux Sums

  • Hall
  • · Replies 14 ·
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14

How to Prove \(\text{vol}_n (B) = \text{vol}_n (B') + \text{vol}_n (B'')\)?

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Infinite series of this type converges?

  • mathman
  • · Replies 5 ·
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5

Undergrad In a 3-dimension isoperimetric problem, a ball maximizes the volume

  • graphking
  • · Replies 6 ·
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6

Undergrad Create a surjective function from [0,1]^n→S^n

  • laurabon
  • · Replies 8 ·
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8

Undergrad Lars Olsen proof of Darboux's Intermediate Value Theorem for Derivatives

  • Hall
  • · Replies 9 ·
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9

Graduate L² norm approximation of Riemann integrable functions by continuous periodic functions

  • physics1000
  • · Replies 5 ·
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5

Undergrad Does topology distinguish between real and imaginary dimensions?

  • Feynstein100
  • · Replies 35 ·
2
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35

Undergrad Proof of i-th Root of i: Analytic Connection?

  • Gear300
  • · Replies 7 ·
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7

Undergrad Why does the identity map induce the identity homomorphism on π₁(X)?

  • Mikaelochi
  • · Replies 2 ·
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2

How to Prove a Complex Number Equation and Its Trajectory Forms a Circle?

  • WMDhamnekar
  • · Replies 2 ·
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2

Graduate What is the significance of the Poincaré conjecture?

  • donglepuss
  • · Replies 1 ·
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1

Undergrad Understanding an argument in Intermediate Value Theorem

  • Hall
  • · Replies 5 ·
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5

Undergrad Applications of complex gamma (or beta) functions in physics?

  • nomadreid
  • · Replies 6 ·
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6

Undergrad Are there any elementary functions of norms that are still norms?

  • askmathquestions
  • · Replies 4 ·
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4

Undergrad Applications of measurement of commutativity

  • askmathquestions
  • · Replies 5 ·
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5

Graduate Standard action of S¹ on Sⁿ

  • WWGD
  • · Replies 64 ·
3
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64

High School Is the Texan Conjecture a mathematical truth or a myth?

  • thetexan
  • · Replies 5 ·
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5

The Supremum of a Set is not an Interior Point

  • OhMyMarkov
  • · Replies 2 ·
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2

Question via email about complex numbers

  • Prove It
  • · Replies 1 ·
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1

Effie's question via email about Complex Numbers

  • Prove It
  • · Replies 2 ·
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2
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1

Sava's question via email about solving complex number equations

  • Prove It
  • · Replies 1 ·
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1

Undergrad If a sequence converges, then all subsequences of it have same limit

  • Hall
  • · Replies 7 ·
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7

How Can I Tackle Difficult Questions Effectively?

  • jaychay
  • · Replies 2 ·
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2

Undergrad How did Archimedes' lemma enter modern real analysis?

  • Gear300
  • · Replies 5 ·
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5

Undergrad Simplify Tricky Equation for Purely Imaginary C with Complex Constants

  • thatboi
  • · Replies 5 ·
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5

Graduate Laurent series for algebraic functions

  • the_pulp
  • · Replies 9 ·
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9

Proving Measure Space Properties of $(X,\bar{\mathcal{B}} ,\bar{\mu})$

  • fabiancillo
  • · Replies 2 ·
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2

Graduate PD code yields two different knot diagrams

  • sophiatev
  • · Replies 3 ·
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3

Undergrad How can I use the concept of a proper map to show that a set is bounded?

  • cbarker1
  • · Replies 18 ·
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18

Undergrad Rewriting the Toeplitz Conjecture

  • MevsEinstein
  • · Replies 7 ·
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7

Undergrad ##\epsilon - \delta## proof and algebraic proof of limits

  • Hall
  • · Replies 48 ·
2
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48

High School Can this decomposition of zeta relate to the Riemann hypothesis?

  • MevsEinstein
  • · Replies 4 ·
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4

Prove that the function is monotonic and not decreasing

  • fabiancillo
  • · Replies 2 ·
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2

High School Is the 10 Dimensional Poincaré Group a Coincidence?

  • Paige_Turner
  • · Replies 2 ·
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2

Graduate What does the metric of a 6D space with 3 compactified dimensions look like?

  • JandeWandelaar
  • · Replies 20 ·
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20

Undergrad Is it valid to express a complex number as a vector?

  • Mayhem
  • · Replies 8 ·
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8

Undergrad The asymptotic behaviour of Elliptic integral near k=1

  • julian
  • · Replies 2 ·
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2

Undergrad I need integrals Int[0,infty]t^(a-1) e^(-t) F(z, e^(-t))dt

  • benorin
  • · Replies 4 ·
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4