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

How Do I Evaluate the Integral \(\int(z^2+1)^2dz\) Over a Cycloid Path?

  • Stumped1
  • · Replies 7 ·
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7

Expand e^{\frac{z}{z-2}} Laurent Series: z=2

  • Stumped1
  • · Replies 3 ·
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3

Proving Divergence of Series \sum_{n=1}^{\infty} \frac{1}{n^{1+i}}

  • Stumped1
  • · Replies 11 ·
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11

Graduate Can Complex Numbers be Compared Using Greater-Than and Less-Than Relations?

  • quawa99
  • · Replies 1 ·
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1

Proof of tan^(-1z) maclauren series

  • Stumped1
  • · Replies 1 ·
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1

Graduate Understanding Disks-and-Bands Surfaces: Genus and Boundary Components

  • WWGD
  • · Replies 2 ·
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2

Graduate Transforming a vector in spherical coordinates

  • SupernerdSven
  • · Replies 1 ·
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1

Cube root of unity with a huge exponent

  • Saitama
  • · Replies 10 ·
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10

How can I show with the definition that f is continuous?

  • evinda
  • · Replies 3 ·
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3
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5

How to Determine Orientation in 3-Dimensional Space?

  • Amer
  • · Replies 1 ·
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1

Using Residue Calculus For a General Cosine Angle

  • shen07
  • · Replies 8 ·
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8

Graduate Interpretation of 'homologous to' - Munkres analysis of homology grou

  • Math Amateur
  • · Replies 12 ·
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12

Graduate Closures of the set of measurable functions

  • Fredrik
  • · Replies 13 ·
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13

Is the set of Natural Numbers Complete?

  • solakis1
  • · Replies 25 ·
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25

Inverse map is closed under complementation

  • carr1
  • · Replies 2 ·
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2
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5

Undergrad Complex Analysis and vector calculus

  • Avatrin
  • · Replies 19 ·
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19

Graduate Homology of Connected Sum of Two Projective Planes, P^2 # P^2

  • Math Amateur
  • · Replies 4 ·
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4

(f_n) converges pointwise to a continuous f

  • evinda
  • · Replies 5 ·
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5

Does \(g \circ f_n \to g \circ f\) Uniformly on \(A\)?

  • evinda
  • · Replies 6 ·
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6

Real life phenomenon that can be modeled by this curve?

  • das1
  • · Replies 5 ·
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5

How to Calculate Matrix Norm in a Banach Space?

  • kalish1
  • · Replies 3 ·
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3

Graduate Question on holomorphic functions

  • disregardthat
  • · Replies 4 ·
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4

Graduate Homology Groups of the Klein Bottle

  • Math Amateur
  • · Replies 1 ·
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1

Why Do the Points from the Mean Value Theorem Depend on Both n and x?

  • evinda
  • · Replies 2 ·
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2

Graduate Does If f be a Measurable Function Imply Finite ∫|f|dm?

  • Funky1981
  • · Replies 8 ·
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8
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3

Can a Function and Its Inverse Prove an Integral Inequality?

  • evinda
  • · Replies 10 ·
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10
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19

Graduate 2D slice of a 6D Calabi-Yau manifold , and other?

  • Spinnor
  • · Replies 7 ·
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7

Graduate Proof of Identity Theorem: Understanding G is Non-Empty

  • disregardthat
  • · Replies 9 ·
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9

Graduate Geometric Derivation of the Complex D-Bar Operator

  • bolbteppa
  • · Replies 1 ·
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1

Riemann Integral: Proving $\int_a^b f = \int_a^c f + \int_c^b f$

  • evinda
  • · Replies 3 ·
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3

Graduate What is the Topology of a Tangent Bundle?

  • MattRob
  • · Replies 6 ·
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6

Show that f+g is integrable and find its value

  • evinda
  • · Replies 2 ·
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2

Show that f is uniformly continuous

  • evinda
  • · Replies 6 ·
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6

Graduate Why Must Any 2-Cycle of the 2D Torus Be of the Form pγ?

  • Math Amateur
  • · Replies 4 ·
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4

What is the Branch Cut for log(z)?

  • Amer
  • · Replies 2 ·
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2

Prove Riemann Integrability: Let f:[0,1]->R

  • mathster
  • · Replies 2 ·
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2

Series Convergence: Showing Convergence & Sum Equivalence

  • mathgirl1
  • · Replies 6 ·
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6

Complex numbers and area of octagon

  • Saitama
  • · Replies 14 ·
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14

No Non-Constant Entire Function $f(z)$ with $Re(f(z))<0$

  • Amer
  • · Replies 3 ·
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3

Graduate Functionla Analysis separability

  • Funky1981
  • · Replies 2 ·
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2

Graduate Understanding Saturated Sets in Quotient Maps

  • hideelo
  • · Replies 4 ·
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4

Graduate Complex Sin value greater than 1

  • tim9000
  • · Replies 12 ·
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12

Graduate The a set is open iff its complement is closed?

  • wotanub
  • · Replies 9 ·
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9

Complete Metric Space: X, d | Analysis/Explanation

  • shen07
  • · Replies 3 ·
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3

Graduate Is R^3 Equivalent to E^3 in Euclidean Space?

  • BHL 20
  • · Replies 6 ·
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6

Show that the limit of f is equal to y

  • evinda
  • · Replies 2 ·
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2
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6
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2

Graduate Fourier series representation for trigonometric and complex form base

  • onceinalifetim
  • · Replies 1 ·
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1

Is $f(z) = \sin(z)/z$ an analytic function on the complex plane?

  • Amer
  • · Replies 7 ·
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7

Map of Area Bounded by y=5x & y=-3x in Upper Plane

  • Amer
  • · Replies 1 ·
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1

Does the Intermediate Value Theorem Apply If h(a) and h(b) Have Opposite Signs?

  • TheDougheyMan
  • · Replies 3 ·
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3

Why is (x,e_i) a zero sequence?

  • mathmari
  • · Replies 2 ·
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2

Graduate Cauchy's differintegral formula

  • Jhenrique
  • · Replies 2 ·
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2

Contraction Map: Proving $f(x)$ is a Contraction

  • onie mti
  • · Replies 1 ·
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1

Graduate What is the Condition for Antiholomorphism?

  • Jhenrique
  • · Replies 2 ·
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2

Solving a Functional Equation Problem: Finding f(3)-f(0)

  • Saitama
  • · Replies 4 ·
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4

Graduate Proof of equality of diameter of a set and its closure

  • chipotleaway
  • · Replies 3 ·
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3

Graduate Mobius Band as a Quotient Topology

  • Math Amateur
  • · Replies 1 ·
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1

Graduate Fundamental groups and arcwise connected spaces.

  • center o bass
  • · Replies 4 ·
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4

Closed infinite orthonormal system

  • mathmari
  • · Replies 2 ·
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2

Undergrad Circles vs an infinitely n-sided polygon.

  • serp777
  • · Replies 20 ·
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20

Is $f_n(x_n) \to f(x)$ Given $f_n \to f$ Uniformly and $x_n \to x$?

  • evinda
  • · Replies 2 ·
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2

Working on lipschitz function and contraction map

  • simo1
  • · Replies 1 ·
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1

Graduate Torus T^2 homeomorphic to S^1 x S^1

  • Math Amateur
  • · Replies 1 ·
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1

Proving |f(x)-f(y)| ≤ K ||x-y|| for f:R^2→R

  • onie mti
  • · Replies 4 ·
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4

Graduate Simple topology problem involving continuity

  • Math Amateur
  • · Replies 3 ·
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3

Graduate Convolution with Complex-Valued Functions: Applications and Limitations

  • mnb96
  • · Replies 4 ·
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4

Graduate What the following statement exactly mean?

  • lee.spi
  • · Replies 4 ·
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4

Undergrad Raising to half power = PRINCIPAL square root?

  • perishingtardi
  • · Replies 2 ·
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2

Graduate Why Banach Spaces Are Important: A Fellow Student's Question

  • Paalfaal
  • · Replies 13 ·
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13

Why is the Infimum of f in Any Subinterval Equal to 0?

  • evinda
  • · Replies 3 ·
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3

Graduate Lebesgue measure in lower dimensional space

  • Shaji D R
  • · Replies 12 ·
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12

Graduate Inverse of the adjoint of the shift operator

  • Likemath2014
  • · Replies 3 ·
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3

Spectral decomposition of compact operators

  • Fermat1
  • · Replies 1 ·
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1

Graduate Dividing Sets in Contact Structures, and Induced Orientations

  • WWGD
  • · Replies 1 ·
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1

Graduate Constructing Atlases: Understanding Topology for GR Class

  • black_hole
  • · Replies 9 ·
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9

About open sets in a metric space.

  • eraldcoil1
  • · Replies 1 ·
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1

Inverse Laplace transform question

  • Dustinsfl
  • · Replies 1 ·
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1

What does zero at infinity mean?

  • Dustinsfl
  • · Replies 1 ·
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1

Region of Convergence: Re${s} > -3 for $\beta$

  • Dustinsfl
  • · Replies 3 ·
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3

Value of Sigma such that the integral converges

  • Dustinsfl
  • · Replies 7 ·
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7

How can I show that the function is continuous at [0,1)U(1,2]?

  • mathmari
  • · Replies 15 ·
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15

Graduate Are residues useful for proper integrals?

  • jinawee
  • · Replies 5 ·
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5

Graduate Solving the Branch Cut Question on f(z) = arccot(z)

  • FelixHelix
  • · Replies 4 ·
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4

Graduate How to Prove Existence of Integer n in Dedekind Cut Using Archimedean Property?

  • Shaji D R
  • · Replies 1 ·
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1

Graduate Gamma Function and the Euler-Mascheroni Constant

  • epr1990
  • · Replies 8 ·
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8

Why Choose Specific Partitions in Integration Proofs?

  • evinda
  • · Replies 2 ·
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2

Graduate What does it mean to use the integrator as an average?

  • sammycaps
  • · Replies 1 ·
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1

Graduate Challenge 14: Smooth is not enough

  • Office_Shredder
  • · Replies 7 ·
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7

Integral Properties of $f^2$: Boundedness?

  • evinda
  • · Replies 6 ·
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6

Find a real number for a continuous function

  • Maxers99
  • · Replies 5 ·
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5

Graduate Is a Metric Space with Infinite Distance Totally Bounded?

  • johnqwertyful
  • · Replies 3 ·
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3

How Does the Linearity of Integration Work for Sum of Functions?

  • evinda
  • · Replies 12 ·
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12
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1

Graduate Test functions for tempered distributions: analytic?

  • jasonRF
  • · Replies 3 ·
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3