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.

Threads

Visualizing an "As Discontinuous As Possible" Function

  • castor28
  • · Replies 12 ·
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12

Graduate How to find the domain of functions of an operator

  • SemM
  • · Replies 19 ·
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19

Remainder converges uniformly to 0

  • mathmari
  • · Replies 10 ·
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10

[Complex Analysis] Singularity in product of analytic functions

  • ludwig1
  • · Replies 1 ·
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1

Undergrad Is there a typo in the formula for dividing complex numbers?

  • Drakkith
  • · Replies 4 ·
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4

How is the remainder for Taylor polynomials calculated?

  • mathmari
  • · Replies 10 ·
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10

Graduate Convergence of an Integral Involving Lebesgue Measure and Sine Functions

  • pawlo392
  • · Replies 10 ·
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10

Limits of functions .... D&K Lemma 1.3.3 .... another question ....

  • Math Amateur
  • · Replies 1 ·
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1

Neccesity and sufficiency .... D&K Lemma 1.3.3 ....

  • Math Amateur
  • · Replies 1 ·
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1

Graduate Covariant derivative and 'see-saw rule'

  • binbagsss
  • · Replies 2 ·
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2

Prove that if g(f(x)) is injective then f is injective

  • cbarker1
  • · Replies 1 ·
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1

Undergrad What is the Difference Between an Angular Sector and a Circular Sector?

  • arlesterc
  • · Replies 3 ·
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3

The Closure of a Set is Closed .... Lemma 1.2.10

  • Math Amateur
  • · Replies 2 ·
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2

Open Subsets of R^n .... D&K Lemma 1.2.5

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Minimum number of moves from a to b

  • BiGyElLoWhAt
  • · Replies 6 ·
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6

Can Derivatives Exist at Discontinuities of a Piecewise Function?

  • mathmari
  • · Replies 40 ·
2
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40

Graduate Sequence induced by short exact sequence

  • PsychonautQQ
  • · Replies 3 ·
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3

High School Spherical Geometry (Two dimension ) Defining a metric

  • Arman777
  • · Replies 11 ·
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11

Undergrad If A is an algebra, then its uniform closure is an algebra.

  • member 587159
  • · Replies 4 ·
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4

Undergrad Describing 3d Manifold Objects as a Hypersurface

  • decentMO
  • · Replies 3 ·
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3

Undergrad What would it even mean to consider a "half" derivative?

  • Ethan Singer
  • · Replies 4 ·
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4

Tanh is uniformly continous on R

  • mathmari
  • · Replies 14 ·
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14

Proving Limits of Exponential Series at Infinity

  • mathmari
  • · Replies 7 ·
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7

High School Nesting of 2-Spheres & 2-Tori in Topological Spaces

  • Wendel
  • · Replies 8 ·
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8

Cauchy-Schwarz Inequality - Duistermaat and Kolk, CH. 1, page 4 .... ....

  • Math Amateur
  • · Replies 1 ·
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1

Multidimensional Real Analysis - Duistermaat and Kolk, Lemma 1.1.7 ....

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad Ordered lattice of topologies on the 3 point set

  • jackferry
  • · Replies 1 ·
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1

High School Complex products: perpendicular vectors and rotation effects

  • Ventrella
  • · Replies 3 ·
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3

Find a function so that the composition is continuous

  • mathmari
  • · Replies 20 ·
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20

Undergrad Can We Mathematically Define Everyday Objects Like Smartphones?

  • Tio Barnabe
  • · Replies 21 ·
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21

Show that the function is bounded and strictly increasing

  • mathmari
  • · Replies 12 ·
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12

Is the Function \( f(x) = \sqrt{4 + x^2} \) Continuous Everywhere?

  • mathmari
  • · Replies 14 ·
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14

Complete Metric Spaces .... Conway, Analysis, Section 5.2 ....

  • Math Amateur
  • · Replies 4 ·
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4

Evaluate Case of Fresnel Integral

  • Deanmark
  • · Replies 13 ·
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13

Graduate What Is the Role of the Boundary Operator in p-Chains?

  • PsychonautQQ
  • · Replies 28 ·
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28

High School How a Klein bottle has a 0 volume?

  • parshyaa
  • · Replies 16 ·
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16

Undergrad Rational sequence converging to irrational

  • Delta2
  • · Replies 13 ·
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13

Can we somehow modify the Lagrange form to get a tighter bound? (Curious)

  • mathmari
  • · Replies 8 ·
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8

Finding the Product of Distinct Roots: A Complex Challenge

  • lfdahl
  • · Replies 1 ·
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1

Additional solution for polar form of complex number

  • TheFallen018
  • · Replies 1 ·
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1

Complex Variables - Max Modulus Inequality

  • joypav
  • · Replies 4 ·
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4

Complex Variables - Solution of a System

  • joypav
  • · Replies 3 ·
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3

Adjoint operator and orthogonal projection

  • mathzero
  • · Replies 3 ·
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3

Undergrad Map from space spanned by 2 complex conjugate vars to R^2

  • Jamz
  • · Replies 5 ·
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5

Undergrad Is simulation considered a type of quantitative analysis?

  • Trixie Mattel
  • · Replies 7 ·
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7

Complex Variables - Zeros of Analytic Functions

  • joypav
  • · Replies 4 ·
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4

Complex Variables - Legendre Polynomial

  • joypav
  • · Replies 2 ·
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2

Graduate Torus 2-sheet covering of Klein bottle

  • PsychonautQQ
  • · Replies 22 ·
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22

High School Is the trefoil knot truly unknottable or is there a way to simplify it?

  • DaveC426913
  • · Replies 13 ·
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13

Reconciling Differences in Vector-Valued Function Derivatives

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Transfinite Taylor series of exp(x) and of h(x)

  • H Tomasz Grzybowski
  • · Replies 6 ·
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6

Where Can I Find a Solution to Zeidler's Eigenvalue Problem?

  • Alone
  • · Replies 7 ·
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7

Graduate Why Does the Orbit Space of a Covering Map Not Necessarily Equal the Base Space?

  • PsychonautQQ
  • · Replies 1 ·
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1

Undergrad Cardinality of fibers same for covering maps

  • PsychonautQQ
  • · Replies 17 ·
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17

Undergrad Choosing points from a set that produce the largest polygon

  • Jeff.Nevington
  • · Replies 5 ·
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5

High School Square root of a negative number in a complex field

  • Adgorn
  • · Replies 45 ·
2
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45

Graduate Fundamental group of a sphere with 6 points removed

  • PsychonautQQ
  • · Replies 15 ·
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15

The Directional Derivative .... in Scalar Fields and Vector Fields ....

  • Math Amateur
  • · Replies 2 ·
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2

How Does Definition 8.9 Imply Differentiability Near Point p?

  • Math Amateur
  • · Replies 1 ·
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1

Differentiation of Vector Valued Functions - Browder, Proposition 8.12 ....

  • Math Amateur
  • · Replies 1 ·
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1

Graduate 8.12 in Browder's "Mathematical Analysis: An Introduction"

  • Math Amateur
  • · Replies 4 ·
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4

Does the Sequence Converge?

  • evinda
  • · Replies 9 ·
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9

Why Does Lemma 8.4 Equal This Expression?

  • Math Amateur
  • · Replies 5 ·
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5

Why Does Theorem 1.9 Use f(t) Instead of f(γ(t))?

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Connected sum of manifolds and free group isomorphisms

  • PsychonautQQ
  • · Replies 15 ·
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15

Recifiable Paths in C .... Conway, Section 1, Ch. 4 ....

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad Why can we define sequences in this fashion?

  • Oats
  • · Replies 2 ·
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2

Insights The Different Faces Of The Special Unitary Group ##SU(2)##

  • fresh_42
  • · Replies 3 ·
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3

A complex numbers' modulus identity.

  • Alone
  • · Replies 1 ·
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1

Understanding Cantor's Theorem and Diameter

  • Math Amateur
  • · Replies 3 ·
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3

Complex Valued Functions BV: John B. Conway Prop 1.3 Explained

  • Math Amateur
  • · Replies 3 ·
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3

Contour Integrals - Example 2.5, Palka, Section 2.2, Ch.4 .... ....

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Questions about Covering maps, manifolds, compactness

  • PsychonautQQ
  • · Replies 1 ·
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1

Understand Proposition 1.3 in Conway's Functions of Complex Variables I

  • Math Amateur
  • · Replies 1 ·
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1

Proof of Lemma 2.1, Part (vi) in Palka's Ch.4: Explaining Inequality

  • Math Amateur
  • · Replies 2 ·
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2

Properties of Contour Integrals - Palka Lemma 2.1 (vi) .... ....

  • Math Amateur
  • · Replies 2 ·
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2

How Can \dot{\gamma}(0) Fail to Exist in Palka's Example 1.3?

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Where can I find a proof of the Swiss cheese theorem?

  • Bestfrog
  • · Replies 5 ·
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5

How does Conway's Theorem 2.29 Derive the Simplified Expression for f(z)?

  • Math Amateur
  • · Replies 2 ·
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2

Insights Representations Of The Special Unitary Group SU(2)

  • fresh_42
  • · Replies 3 ·
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3

Complex number geometrical problem

  • amr21
  • · Replies 4 ·
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4

Mapping of a Circle in the Complex Plane

  • amr21
  • · Replies 7 ·
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7

Proof of Divergence: (-1)^n Sequence

  • solakis1
  • · Replies 8 ·
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8

Do we distinguish cases for n?

  • evinda
  • · Replies 12 ·
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12

Analytic Functions - Palka, Ch. III, Section 1.3 ....

  • Math Amateur
  • · Replies 2 ·
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2

High School Understanding the Inconsistencies of Imaginary Numbers

  • Tian En
  • · Replies 6 ·
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6

How Can We Prove the Modified Bernoulli Inequality?

  • evinda
  • · Replies 6 ·
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6

Graduate Fundamental group of n connect tori with one point removed

  • PsychonautQQ
  • · Replies 9 ·
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9

Undergrad Intuition behind induced homomorphism from covering maps

  • PsychonautQQ
  • · Replies 15 ·
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15

Graduate Fundamental group of Project Plane with 2 points missing

  • PsychonautQQ
  • · Replies 6 ·
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6

Disconnected Sets .... Palka, Lemma 3.1 ....

  • Math Amateur
  • · Replies 2 ·
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2

Limits of Complex Functions .... Final Remark from Palka in Section 2.2 ....

  • Math Amateur
  • · Replies 2 ·
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2

Limits of Complex Functions .... Example from Palka ....

  • Math Amateur
  • · Replies 2 ·
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2

Continuity of Complex Functions .... ....

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Impossible to lift the identity map on the circle

  • PsychonautQQ
  • · Replies 3 ·
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3

Undergrad Understanding Compactness in ##R^2##: Analyzing Boundaries and Open Disks

  • FallenApple
  • · Replies 12 ·
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12

Undergrad Retract of a connected space is connected

  • PsychonautQQ
  • · Replies 6 ·
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6

Undergrad Proof that retract of Hausdorff space is closed

  • PsychonautQQ
  • · Replies 1 ·
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1

Undergrad How Does Closure in a Neighborhood Imply Membership in a Set?

  • PsychonautQQ
  • · Replies 12 ·
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12

The Residue Theorem To Evaluate Integrals

  • joypav
  • · Replies 5 ·
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5