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.

Sub-forums

Threads

Graduate Math & David Hume: Tangents & Circles

  • thinkandmull
  • · Replies 3 ·
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3

Complex numbers and conjugates

  • Sean1
  • · Replies 2 ·
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2

Understanding Open/Closed Sets in $\mathbb{R}^n$

  • evinda
  • · Replies 13 ·
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13

How Does a Quasi-Nonexpansive Operator Function in Metric Spaces?

  • ozkan12
  • · Replies 1 ·
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1

No Max for Functions: Examples & Explanations

  • evinda
  • · Replies 23 ·
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23

Kannan mapping and quasi-nonexpansive mapping

  • ozkan12
  • · Replies 7 ·
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7

Undergrad Finding solution of equation in complex domain?

  • cdummie
  • · Replies 4 ·
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4

Contractive Mappings: Unique Fixed Point & Notation Questions

  • ozkan12
  • · Replies 1 ·
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1

How Do Laurent Series Differ from Taylor Series in Complex Analysis?

  • ognik
  • · Replies 1 ·
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1

Is $\ell^\infty$ a Compact Metric Space?

  • ozkan12
  • · Replies 1 ·
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1

Graduate Does T have a unique fixed point in X?

  • Samuel Williams
  • · Replies 4 ·
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4
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8

Proving $T:X\to X$ is not a Contraction on $X=[1, \infty)$

  • ozkan12
  • · Replies 7 ·
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7

Graduate Complex Mapping - Is transforming boundaries enough?

  • davidbenari
  • · Replies 5 ·
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5

What is the limit of a circumference as the power approaches infinity?

  • Julio1
  • · Replies 2 ·
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2

Graduate ##\int \frac{dz}{z} ## along a line on the complex plane

  • davidbenari
  • · Replies 10 ·
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10

Graduate A path which its domain is a general compact set.

  • MathematicalPhysicist
  • · Replies 6 ·
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6

Cauchy sequence in fixed point theory

  • ozkan12
  • · Replies 22 ·
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22

Non Increasing and Decreasing Sequence

  • ozkan12
  • · Replies 9 ·
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9

Is Non-Increasing the Same as Decreasing?

  • ozkan12
  • · Replies 9 ·
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9

Increasing, non-increasing, decreasing and non-decreasing functions

  • ozkan12
  • · Replies 6 ·
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6

Undergrad What does the term "pointwise" refer to?

  • Mr Davis 97
  • · Replies 5 ·
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5

Graduate Learning Topology: Problem Solving & Book Recommendations

  • Avatrin
  • · Replies 12 ·
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12

Undergrad Why Do Algebraic Continuity Theorems Confuse Me?

  • Of Mike and Men
  • · Replies 4 ·
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4

Graduate Distributions on non-test functions

  • pellman
  • · Replies 4 ·
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4

Graduate Distributions & test functions in specific applications

  • jasonRF
  • · Replies 2 ·
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2

Graduate What is the intuitive meaning of continuity in topology?

  • kade
  • · Replies 19 ·
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19

Graduate Proving the Limit of a Sequence is Unique: Real Analysis Class

  • B3NR4Y
  • · Replies 4 ·
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4

Proof of Supremum of $M$ Mapping into Itself

  • ozkan12
  • · Replies 5 ·
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5

Graduate Points on a Plane: Representation with 1 or 2 Real Numbers?

  • jeremy22511
  • · Replies 3 ·
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3

Generalization of Banach contraction principle

  • ozkan12
  • · Replies 1 ·
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1

Contraction constant in banach contraction principle

  • ozkan12
  • · Replies 3 ·
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3

Continuous mapping and fixed point

  • ozkan12
  • · Replies 6 ·
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6

Proof of Banach-Caccioppoli theorem

  • ozkan12
  • · Replies 10 ·
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10

Proof of Contraction Mapping for $f\left(x\right)={e}^{{-e}^{-x}}$

  • ozkan12
  • · Replies 12 ·
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12

Undergrad Define the complex number Z = u^v

  • Bruno Tolentino
  • · Replies 6 ·
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6

Undergrad Complex numbers and negative roots

  • alvin51015
  • · Replies 28 ·
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28

Graduate Confusion about definition of compactness

  • Chain
  • · Replies 8 ·
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8

Graduate Why isnt Cauchy's formula used for the perimeter of ellipse?

  • Austin Daniel
  • · Replies 9 ·
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9

Undergrad Complex numbers and beyond....

  • Bruno Tolentino
  • · Replies 3 ·
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3

Show Metric Proves All Points Inside Circle Have Same Center

  • Julio1
  • · Replies 2 ·
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2

Please check Residue theorem excercise

  • ognik
  • · Replies 8 ·
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8

Undergrad How Many Spanning Trees Can a Graph Have?

  • Marvin94
  • · Replies 1 ·
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1

Graduate What is a derivative in the distribution sense?

  • pellman
  • · Replies 2 ·
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2

Graduate Is Category Theory Really Useless for Building Versatile Scientific Models?

  • hepiaaro
  • · Replies 7 ·
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7

Graduate Does Bott periodicity imply homotopy equivalences?

  • nonequilibrium
  • · Replies 1 ·
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1

Proof of Cauchy Integral formula

  • ognik
  • · Replies 4 ·
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4

Zero Integral Implies Zero Function

  • Julio1
  • · Replies 2 ·
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2

Generalized triangle inequality in b-metric spaces

  • ozkan12
  • · Replies 3 ·
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3

Triangle inequality in b-metric spaces

  • ozkan12
  • · Replies 11 ·
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11

Find coefficiant of Laurent series, without using residue

  • ognik
  • · Replies 1 ·
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1

Graduate Sufficient condition for the density

  • Flem
  • · Replies 1 ·
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1
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5

Please check find residue problem

  • ognik
  • · Replies 2 ·
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2

Graduate Are all smooth functions square-integrable?

  • pellman
  • · Replies 2 ·
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2

Graduate Entire Functions and Lacunary Values.

  • WWGD
  • · Replies 8 ·
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8
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8

Path dependance of complex conjugate

  • ognik
  • · Replies 16 ·
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16

Understanding the Laurent Series of $\frac{1}{z(z-1)(z-2)}$

  • ognik
  • · Replies 4 ·
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4

Graduate How does this statement follow? (adjoints on Hilbert spaces)

  • pellman
  • · Replies 1 ·
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1

Graduate What happens when two identical one-sided objects are merged in space?

  • Observeraren
  • · Replies 2 ·
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2

Graduate What is the Nature of Singularity in the Function f(x)=exp(-1/z)?

  • ion santra
  • · Replies 2 ·
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2

Cauchy Integral Theorem with partial fractions

  • ognik
  • · Replies 2 ·
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2

Graduate How does one-to-oneness follow from this?

  • pellman
  • · Replies 2 ·
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2

High School I think I'm missing something in this complex number problem

  • JR Sauerland
  • · Replies 9 ·
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9

Graduate How does the idea of entropy relate to something like E8

  • Jimster41
  • · Replies 5 ·
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5

Undergrad Proof of Infinite Set of Real Numbers Between Two Unequal Real Numbers

  • RandomAllTime
  • · Replies 18 ·
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18

Graduate Why my endomorphisme between Polynomial fonction is not continuous?

  • Calabi
  • · Replies 6 ·
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6

Intuition for inverse hyperbolics

  • ognik
  • · Replies 3 ·
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3

1st Derivative of Cauchy Integral formula

  • ognik
  • · Replies 2 ·
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2

Contour integral representation of Kronecker delta

  • ognik
  • · Replies 2 ·
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2

Reverse direction for complex functions

  • ognik
  • · Replies 4 ·
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4

Undergrad Is a Perfect Circle Possible Given the Limitations of Pi and Space?

  • Josh S Thompson
  • · Replies 54 ·
2
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54

Tricky Complex number simplification

  • ognik
  • · Replies 2 ·
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2
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4

Graduate Group theory? This solution doesn't make sense....

  • applestrudle
  • · Replies 2 ·
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2

Graduate Understand Successive Bisection for Theorem Proof

  • elliti123
  • · Replies 10 ·
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10

Undergrad Fundamental theorem of algebra and factoring?

  • pellman
  • · Replies 6 ·
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6

Reverse triangle inequality with a + sign

  • ognik
  • · Replies 2 ·
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2

Do Cauchy-Riemann Conditions Guarantee Analyticity?

  • ognik
  • · Replies 1 ·
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1

Graduate Solve Endomorphism Sequence Questions in a Vectoriel Space

  • Calabi
  • · Replies 7 ·
Replies
7

Understanding the Concept of Double Conjugate in Complex Functions

  • ognik
  • · Replies 2 ·
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2

Graduate Question on dense subset of l^p space

  • kostas230
  • · Replies 6 ·
Replies
6

Graduate Questioning an assumption in calculus of variations

  • hideelo
  • · Replies 4 ·
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4

Undergrad Mathematical insight about waves

  • Mappe
  • · Replies 6 ·
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6

Graduate Fourier Series: Understanding Non-Periodic Signals

  • tim9000
  • · Replies 6 ·
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6

Proving d(x,A) ≤ d(x,y) + d(y,A) in Metric Spaces

  • ozkan12
  • · Replies 1 ·
Replies
1

Graduate Weierstrass p-Function Asympototics?

  • "pi"mp
  • · Replies 5 ·
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5

Find Roots of sin z: Solutions & Explanations

  • ognik
  • · Replies 3 ·
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3

Outer measure exclusion of zero set question

  • Tom555
  • · Replies 2 ·
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2

Graduate Nonlinear constrained optimization - how?

  • maistral
  • · Replies 19 ·
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19

Undergrad Why are Real Numbers Often Referred to as Points in Mathematical Functions?

  • shuxue
  • · Replies 2 ·
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2

Graduate Real part of this complex quantity

  • giuliopascal
  • · Replies 3 ·
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3

Prove sinh(z) Identity: Show |sinh(z)|^2 = sin^2x + sinh^2y

  • ognik
  • · Replies 1 ·
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1

Graduate Motivation of sin and cos functions

  • Mappe
  • · Replies 5 ·
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5

Graduate Rigorousness of this Dirac delta formula

  • ShayanJ
  • · Replies 20 ·
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20

Graduate How many topologies exist on 4 points? Any nomenclature?

  • Cruikshank
  • · Replies 3 ·
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3

Graduate Question about a flat torus topology

  • Jimster41
  • · Replies 21 ·
Replies
21

Graduate ....they say it's very difficult to show what sqrt2 is....

  • strobeda
  • · Replies 8 ·
Replies
8

Graduate Evaluating a limit of a function of two variables

  • Cristopher
  • · Replies 1 ·
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1