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 Uniform continuity and the sup norm

  • AxiomOfChoice
  • · Replies 2 ·
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Graduate The set of the real numbers is closed

  • tom.stoer
  • · Replies 14 ·
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14

Closed form chains of derivatives

  • mathbalarka
  • · Replies 10 ·
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10

Undergrad Complex numbers: reinventing the wheel?

  • bobie
  • · Replies 12 ·
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12

Graduate Understanding Contractible Curves

  • sadegh4137
  • · Replies 2 ·
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2

Graduate Construct an explicit isomorphism

  • bedi
  • · Replies 1 ·
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1

Graduate Are There Subsets of the Real Line That Are Compact But Not Connected?

  • Salamon
  • · Replies 7 ·
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7

Graduate Open set (equivalent definitions?)

  • center o bass
  • · Replies 3 ·
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3

Graduate How can the residue theorem be used to calculate contour integrals?

  • HJ Farnsworth
  • · Replies 4 ·
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4

Graduate Is Euclid's Fourth Postulate Redundant?

  • lugita15
  • · Replies 3 ·
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How Do I Prove the Cantor-Bernstein Theorem?

  • Usagi
  • · Replies 2 ·
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2

Expressing zeta(3) in terms of a Glaisher-Kinkelin-like constant

  • polygamma
  • · Replies 1 ·
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Graduate Examples of Diminnie orthogonality

  • PonyBarometer
  • · Replies 1 ·
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1

Graduate Constructing the real number system by Dedekind cuts?

  • Vahsek
  • · Replies 11 ·
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A derivation of the duplication formula for the Barnes-G function

  • polygamma
  • · Replies 2 ·
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Graduate {R. Zeta fn. zeros} = {Dir. eta fn. zeros} for 0<Re(s)<1?

  • nomadreid
  • · Replies 4 ·
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4

Graduate Cauchy-Goursat Theorem question

  • mathsciguy
  • · Replies 1 ·
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1

Graduate Simplifying an Infinite Composite Recursion in a System of Equations

  • Spacemoss
  • · Replies 4 ·
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4

Show that the function is not differentiable at the point z

  • mathmari
  • · Replies 5 ·
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5

Undergrad Challenge 10a: Temperatures of the Earth

  • Office_Shredder
  • · Replies 8 ·
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8

Graduate The windowed Fourier transform on R

  • m.a.math
  • · Replies 2 ·
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2

Show that f'(0) exists and find its value

  • evinda
  • · Replies 9 ·
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9

High School Any real world use of imaginary numbers?

  • suchal
  • · Replies 21 ·
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21

Generalized Log-Trig series related to the Hurwitz Zeta

  • DreamWeaver
  • · Replies 11 ·
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11

Trigonometric series related to the Hurwitz Zeta function

  • DreamWeaver
  • · Replies 11 ·
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11

Graduate Equicontinuity at a point if.f. continuous function constant

  • adam512
  • · Replies 3 ·
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3

Graduate Are resolvents for self-adjoint operators themselves self-adjoint?

  • AxiomOfChoice
  • · Replies 2 ·
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2

Graduate Which algebraic branches does a pochammer contour traverse?

  • jackmell
  • · Replies 2 ·
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2

A conjecture on a Generalized Barnes' function - can anyone help?

  • DreamWeaver
  • · Replies 9 ·
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9

Graduate Defining the square root of an unbounded linear operator

  • AxiomOfChoice
  • · Replies 5 ·
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5

Graduate Are Absolute Harmonicity and Analyticity Related in Functions?

  • rasi
  • · Replies 1 ·
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How Can One Prove the Besicovitch Covering Lemma for an Unbounded Set?

  • ArcanaNoir
  • · Replies 1 ·
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1

If Derivative is Not Zero Anywhere Then Function is Injective.

  • caffeinemachine
  • · Replies 6 ·
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6

Undergrad Is Adult Rudin Suitable for Self-Study of Complex Analysis?

  • pswongaa
  • · Replies 1 ·
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1

Proving Simple Summable Functions and Cauchy Sequences on [0,1]

  • Fermat1
  • · Replies 11 ·
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11

Graduate Why Must Cuts in the Rationals Have No Largest Element?

  • Demon117
  • · Replies 1 ·
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Graduate Find Analytic Functions with u(x,y)=(x^2)+(y^2)

  • rasi
  • · Replies 5 ·
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5

Graduate Is the closure of a set the same as its smallest closed set containing it?

  • Bipolarity
  • · Replies 1 ·
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Graduate Identifying singularities of f and classifying them

  • SALAAH_BEDDIAF
  • · Replies 3 ·
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3

Proving Y is Dense in X: Let's See!

  • Fermat1
  • · Replies 5 ·
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5

Graduate Definition of two homeomorphic spaces

  • Streltsy
  • · Replies 9 ·
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9

Poles on Real Line: Is \(z = \pm a\) Included?

  • Dustinsfl
  • · Replies 2 ·
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Prove u(A/E)=0 for Compact Hausdorff Spaces and Borel Measure

  • Fermat1
  • · Replies 4 ·
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4

Norm of a Bounded Linear Functional

  • Sudharaka
  • · Replies 8 ·
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8

Graduate Definition of a subbasis of a topology

  • V0ODO0CH1LD
  • · Replies 4 ·
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4

Complex Number Problems in Applied Maths

  • anil86
  • · Replies 4 ·
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Measurability of Open Sets in [0,1]

  • Fermat1
  • · Replies 2 ·
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Graduate Measurability with respect to completion

  • haljordan45
  • · Replies 4 ·
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Graduate What is ramification for z^(p/q)(1-z)^(r/s)?

  • jackmell
  • · Replies 1 ·
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Can the Dominated Convergence Theorem Apply to f_n(x) on [0,1]?

  • Fermat1
  • · Replies 4 ·
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4

Show that the sequence has a decreasing subsequence

  • mathmari
  • · Replies 3 ·
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3

Graduate Are the positive-semidefinite requirements necessary for metric space axioms?

  • Bipolarity
  • · Replies 19 ·
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19

Graduate Can the topology of a manifold influence its metric properties?

  • friend
  • · Replies 11 ·
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11

Graduate Is the empty set always part of the basis of a topology?

  • V0ODO0CH1LD
  • · Replies 18 ·
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18

Graduate Questions about the definition of open sets

  • V0ODO0CH1LD
  • · Replies 5 ·
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5

Graduate Is There a More Rigorous Analysis Text Than Rudin?

  • bhagwad
  • · Replies 30 ·
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Graduate Poor Symbol choice - Principles of Mathematical Analysis by Rudin

  • bhagwad
  • · Replies 4 ·
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4
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Graduate Modified Bessel function with imaginary index is purely real?

  • perishingtardi
  • · Replies 1 ·
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1

Using Classification of Poles to Calculate Residues

  • shen07
  • · Replies 9 ·
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9

Graduate How to Express Function f in Terms of Complex Variable z?

  • SALAAH_BEDDIAF
  • · Replies 3 ·
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3

Examples of Uniformly, point wise convergence

  • Amer
  • · Replies 2 ·
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Graduate Understanding Complex Integrals: Interpretation and Visualization

  • Jhenrique
  • · Replies 6 ·
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6

Graduate Advanced numerical analysis - numerical integration

  • alpha754293
  • · Replies 2 ·
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2

Graduate Why Does B Include the Segment [a,c) in Topological Space X?

  • qinglong.1397
  • · Replies 2 ·
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High School Why is i^2 equal to -1 in complex numbers?

  • Tyrion101
  • · Replies 18 ·
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18
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3

Graduate Is there a relation between log and arcs for complex numbers?

  • Jhenrique
  • · Replies 9 ·
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9

Solving Complex Integration Problems with \((*) Formula

  • Dustinsfl
  • · Replies 6 ·
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6

Product of discontinuous functions

  • alyafey22
  • · Replies 3 ·
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3

Coefficient in a Laurent Expansion in terms of an Integral

  • shen07
  • · Replies 7 ·
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7

Graduate Isolated points must be boundary points?

  • Bipolarity
  • · Replies 3 ·
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3

Convergence of bounded linear operators

  • Fermat1
  • · Replies 6 ·
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6

Limit of f(x+y)=f(x)+f(y) near 0

  • alyafey22
  • · Replies 18 ·
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18

Graduate Rudin Theorem 1.21. How does he get The identity ?

  • bhagwad
  • · Replies 6 ·
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6

Integral = 2pi sum res UHP + pi i sum res real axis

  • Dustinsfl
  • · Replies 5 ·
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5

Graduate How to think of uniform continuity intuitively?

  • math.geek
  • · Replies 18 ·
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18

Complex real function u when f = u + iv

  • Dustinsfl
  • · Replies 7 ·
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7

Undergrad What does a function takes on mean?

  • Nikitin
  • · Replies 1 ·
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1

Graduate Bijection is uniformly continuous

  • deekin
  • · Replies 1 ·
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1

How can I solve power series questions 1a, 1c, and 1f?

  • nacho-man
  • · Replies 6 ·
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6

Residues/Classifying singularities

  • nacho-man
  • · Replies 1 ·
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1

What is the residue of a complex integral with a double pole at infinity?

  • Dustinsfl
  • · Replies 1 ·
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1

Residue Calculus: Solving Integrals with Sinusoidal Functions

  • Dustinsfl
  • · Replies 1 ·
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1

Graduate Can someone explain the need for Laurent series in complex analysis?

  • Nikitin
  • · Replies 10 ·
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10
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1

High School What is the Best Book on Complex Numbers for Beginners?

  • rohit dutta
  • · Replies 1 ·
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1

Complete spaces and Cauchy sequences

  • alyafey22
  • · Replies 4 ·
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4

Simplifying a Legendre polynomial

  • Dustinsfl
  • · Replies 2 ·
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2

A curiosity about the Riemann Zeta Function....

  • chisigma
  • · Replies 10 ·
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10

Neighbourhood of Convergence of Sequence

  • Sudharaka
  • · Replies 20 ·
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20

Undergrad Maclaurin series of an elementary function question

  • Crake
  • · Replies 1 ·
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1

Graduate How does the choice of branch cut affect the values of a multi-valued function?

  • dipole
  • · Replies 7 ·
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7

Proving Divergence of $\cos(n)$ w/ Definition of Limits

  • alyafey22
  • · Replies 2 ·
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2

Graduate All real numbers are complex numbers?And are I #'s orthogonal R#'s?

  • nabeel17
  • · Replies 7 ·
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7

Graduate Compact embedding and dense embedding

  • Tatianaoo
  • · Replies 4 ·
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4

Is A Measurable if the Inner and Outer Measures are Equal?

  • ryo0071
  • · Replies 3 ·
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3