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

Undergrad A differential geometry question from continuum mechanics

  • wrobel
  • · Replies 18 ·
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18

Graduate Zeros of functions analytic in 2 variables

  • Paul Colby
  • · Replies 6 ·
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6

Undergrad What is "x" in this definition of a basis?

  • Hill
  • · Replies 4 ·
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4

Graduate Knots In 4D

  • Hornbein
  • · Replies 2 ·
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2

Graduate A nice YouTube channel about all things Riemann Zeta

  • Swamp Thing
  • · Replies 1 ·
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1

Undergrad About the definition of topological manifold using closed sets

  • cianfa72
  • · Replies 14 ·
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14

Graduate Trivial fiber bundle vs product space

  • cianfa72
  • · Replies 31 ·
2
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31

Graduate Another similar notion to compactness

  • mad mathematician
  • · Replies 2 ·
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2

Graduate Hopf fibration of 3-sphere

  • cianfa72
  • · Replies 39 ·
2
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39

Graduate Shauder basis for Hilbert spaces

  • cianfa72
  • · Replies 0 ·
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0

Undergrad Finding the inverse tangent of a complex number

  • bsaucer
  • · Replies 3 ·
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3

Undergrad Apparent counterexample to Cauchy-Goursat theorem (Complex Analysis)

  • SomeBody
  • · Replies 7 ·
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7

Undergrad 2-sphere intrinsic definition by gluing disks' boundaries

  • cianfa72
  • · Replies 11 ·
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11

Undergrad Confused by proof in Hocking and Young

  • yossell
  • · Replies 4 ·
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4

Undergrad "Magic" regulating functions for divergent series

  • Swamp Thing
  • · Replies 3 ·
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3

High School How does the Riemann Hypothesis/Riemann Zeta function even work?

  • Beyond3D
  • · Replies 17 ·
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17

Graduate Question about intersection of coordinate rings

  • MathLearner123
  • · Replies 1 ·
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1

Undergrad How are the following three definitions subtly different?

  • elias001
  • · Replies 15 ·
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15

Undergrad Evaluate two complex integrals along a parabolic contour

  • elias001
  • · Replies 2 ·
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2

Undergrad Convergence not defined by any metric

  • elias001
  • · Replies 17 ·
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17

Undergrad Homemorphism in quotient topology

  • elias001
  • · Replies 5 ·
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5

Undergrad No structure in ##(d,x)## in ##\textbf{Met*}(X)## is admissible

  • elias001
  • · Replies 0 ·
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0

Undergrad A beginner’s thoughts on rotation number -- Resource suggestion request

  • Pencilvester
  • · Replies 6 ·
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6

Insights The Many Faces of Topology

  • fresh_42
  • · Replies 3 ·
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3

Undergrad (0,1) is uncountable using binary expansions?

  • psie
  • · Replies 15 ·
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15

Graduate Expansion with respect to ##z_1##

  • MathLearner123
  • · Replies 1 ·
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1

Undergrad What is the 4D Equivalent of a Möbius Strip or Klein Bottle?

  • blackholesarecool
  • · Replies 30 ·
2
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30

Undergrad In Which N-Dimensional Spaces Are Rotations Chiral?

  • Hornbein
  • · Replies 11 ·
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11

High School Functions f: ℝ --> ℝ

  • mairzydoats
  • · Replies 8 ·
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8

Undergrad How to see that cos(z) is unbounded, but cos(xy)+isin(xy) is bounded?

  • am4th
  • · Replies 8 ·
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8

Undergrad Continuity of linear map from subspace of Euclidean space

  • psie
  • · Replies 2 ·
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2

Undergrad Uniform convergence of difference quotient in higher dimensions

  • psie
  • · Replies 1 ·
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1

Graduate A complicated integral to be evaluated by complex contour method

  • Bengy
  • · Replies 14 ·
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14

Undergrad Dyadic cubes generate Borel sigma algebra of subset

  • psie
  • · Replies 2 ·
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2

High School Topological neigborhoods that are not intervals in the real line?

  • mcastillo356
  • · Replies 15 ·
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15

Undergrad Homeomorphism onto a not open image in the target

  • cianfa72
  • · Replies 2 ·
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2

Undergrad On commutativity of convolution

  • psie
  • · Replies 3 ·
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3

Undergrad A concise "proof" of the Riemann-Lebesgue lemma

  • psie
  • · Replies 1 ·
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1

Undergrad A curve that does not meet rational points

  • wrobel
  • · Replies 9 ·
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9

Undergrad Relation between a circle and line in complex plane

  • Darshit Sharma
  • · Replies 16 ·
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16

Undergrad About convergence of complex power series on the circle ##|z - z_0|=r##

  • cianfa72
  • · Replies 22 ·
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22

Graduate Information theory via knot theory

  • Twodogs
  • · Replies 15 ·
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15

Undergrad Connection between absolute continuity of function and measure

  • psie
  • · Replies 2 ·
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2

Undergrad Pointwise convergence in Lp space

  • psie
  • · Replies 1 ·
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1

Undergrad Norm of integral less than or equal to integral of norm of function

  • psie
  • · Replies 3 ·
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3

High School Continuity of ln(x) function

  • eneacasucci
  • · Replies 11 ·
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11

Undergrad How to show the diagonal in the extended plane is closed?

  • psie
  • · Replies 4 ·
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4

Undergrad Verifying pointwise convergence of indicator functions

  • psie
  • · Replies 4 ·
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4

Undergrad Measure with respect to complete measure is also complete

  • psie
  • · Replies 3 ·
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3

Undergrad Help understanding a passage from a proof of change of variables formula

  • psie
  • · Replies 1 ·
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1

Undergrad Metric Tensor on ##S^1## x ##S^2##

  • Onyx
  • · Replies 6 ·
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6

Undergrad Unit sphere is compact in 1-norm

  • psie
  • · Replies 3 ·
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3

Undergrad Zero raised to a positive real number

  • psie
  • · Replies 12 ·
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12

Undergrad Exercise 2.23 in Folland's real analysis text

  • psie
  • · Replies 2 ·
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2

Undergrad Does Ricci Flow Contract a 3-Sphere to Its Center?

  • casparov
  • · Replies 1 ·
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1

Undergrad On base-b expansion of nonnegative reals

  • psie
  • · Replies 7 ·
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7

Undergrad On translation and dilation invariant Lebesgue measure: Folland's text

  • psie
  • · Replies 2 ·
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2

Undergrad Simple partitioning of sequence in Proposition 1.15 in Folland's text

  • psie
  • · Replies 3 ·
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3

Undergrad Regarding dominated convergence theorem in Folland

  • psie
  • · Replies 5 ·
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5

Undergrad On Borel sets of the extended reals

  • psie
  • · Replies 2 ·
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2

High School Can Riemann integrable be defined using the epsilon delta non method?

  • hongseok
  • · Replies 5 ·
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5

Undergrad Basic question on 'bounded implies totally bounded'

  • psie
  • · Replies 16 ·
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16

Undergrad Open balls dense in closed balls in Euclidean space

  • psie
  • · Replies 2 ·
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2

Insights Views On Complex Numbers

  • fresh_42
  • · Replies 108 ·
4
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108

Undergrad Show that a "cross" is not a topological manifold

  • cianfa72
  • · Replies 20 ·
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20

Undergrad Tough lemma on locally finite refinement

  • Korybut
  • · Replies 8 ·
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8

Insights Aspects Behind the Concept of Dimension in Various Fields

  • fresh_42
  • · Replies 2 ·
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2

Graduate Cubical cup poduct with a unit 1-cochain and the coboundary operator

  • CoreSpace
  • · Replies 0 ·
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0

Undergrad Compact support functions and law of a random variable

  • psie
  • · Replies 11 ·
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11

Undergrad Question about partial derivative relations for complex numbers

  • binbagsss
  • · Replies 9 ·
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9

Undergrad Uniform closure of algebra of bounded functions is uniformly closed

  • psie
  • · Replies 2 ·
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2

Undergrad Parallel rectangles contained in oblique rectangle

  • psie
  • · Replies 5 ·
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5

Graduate Question about different statements of Picard Theorem

  • MathLearner123
  • · Replies 0 ·
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0

Undergrad Question about convex property in Jensen's inequality

  • psie
  • · Replies 4 ·
Replies
4

Undergrad A non-empty intersection of closures of level sets implies discontinuity

  • pasmith
  • · Replies 1 ·
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1

Graduate Proving that this integral is divergent

  • cbarker1
  • · Replies 2 ·
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2

Graduate Question about covering map of punctured unit disk

  • MathLearner123
  • · Replies 3 ·
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3

Graduate Question about lifting of a function

  • MathLearner123
  • · Replies 2 ·
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2

Graduate Question about existence of path-lifting property

  • MathLearner123
  • · Replies 8 ·
Replies
8

Undergrad Riemann integrability and uniform convergence

  • lys04
  • · Replies 2 ·
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2

Integration in Polar Coordinates (Fubini/Tonelli)

  • joypav
  • · Replies 4 ·
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4

Undergrad On theorem 1.19 in Folland's and completion of measure

  • psie
  • · Replies 1 ·
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1

Undergrad Formal definition of multiplication for real and complex numbers

  • logicgate
  • · Replies 2 ·
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2

High School Identity Theorem for power series

  • Hill
  • · Replies 10 ·
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10

Undergrad Are slices of measurable functions measurable?

  • Office_Shredder
  • · Replies 3 ·
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3

Undergrad Post your favorite real analysis problem

  • docnet
  • · Replies 5 ·
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5

Undergrad On integral of simple function and representation

  • psie
  • · Replies 6 ·
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6

Undergrad Collection of finite unions of half-open intervals form an algebra

  • psie
  • · Replies 3 ·
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3

Undergrad How Does the Hopf Map Relate to Foliation and Knot Theory on the 3-Torus?

  • Anko
  • · Replies 8 ·
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8

Undergrad Help with basic transfinite induction proof

  • psie
  • · Replies 2 ·
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2

Undergrad On two definitions of locally compact

  • psie
  • · Replies 5 ·
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5

Undergrad Showing equivalence of two definitions of essential supremum

  • psie
  • · Replies 1 ·
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1

Undergrad Two basic results from measure theory -- on volumes of rectangles

  • psie
  • · Replies 2 ·
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2

Undergrad In which sense(s) do square integrable functions go to zero at infinity?

  • gentzen
  • · Replies 2 ·
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2

Graduate Functional Analysis for Physics in 2024

  • psterphysics
  • · Replies 11 ·
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11

Undergrad Question about branch of logarithms

  • MathLearner123
  • · Replies 14 ·
Replies
14

Graduate Can Equilibrium State Determine Complex Potential?

  • binbagsss
  • · Replies 5 ·
Replies
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