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

4.6K threads

Threads

How Do You Calculate the Real and Imaginary Parts of \( e^{e^z} \)?

  • Deanmark
  • · Replies 1 ·
Replies
1

Duistermaat and Kolk Example 1.3.8: proving f(ℝ) = [-1, 1]

  • Math Amateur
  • · Replies 2 ·
Replies
2

Graduate How can I Prove the following Integral Inequality?

  • zarei175
  • · Replies 2 ·
Replies
2

Visualizing an "As Discontinuous As Possible" Function

  • castor28
  • · Replies 12 ·
Replies
12

Graduate How to find the domain of functions of an operator

  • SemM
  • · Replies 19 ·
Replies
19

Remainder converges uniformly to 0

  • mathmari
  • · Replies 10 ·
Replies
10

[Complex Analysis] Singularity in product of analytic functions

  • ludwig1
  • · Replies 1 ·
Replies
1

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

  • Drakkith
  • · Replies 4 ·
Replies
4

How is the remainder for Taylor polynomials calculated?

  • mathmari
  • · Replies 10 ·
Replies
10

Graduate Convergence of an Integral Involving Lebesgue Measure and Sine Functions

  • pawlo392
  • · Replies 10 ·
Replies
10

Proving necessity in D&K Lemma 1.3.3 on limits

  • Math Amateur
  • · Replies 1 ·
Replies
1

Necessary and sufficient conditions in Duistermaat-Kolk lemma 1.3.3

  • Math Amateur
  • · Replies 1 ·
Replies
1

Graduate Covariant derivative and 'see-saw rule'

  • binbagsss
  • · Replies 2 ·
Replies
2

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

  • cbarker1
  • · Replies 1 ·
Replies
1

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

  • arlesterc
  • · Replies 3 ·
Replies
3

Why does A closure equal complement of interior of complement imply A is closed?

  • Math Amateur
  • · Replies 2 ·
Replies
2

Why is Lemma 1.2.5 restricted to finite collections of open subsets?

  • Math Amateur
  • · Replies 2 ·
Replies
2

Undergrad Minimum number of moves from a to b

  • BiGyElLoWhAt
  • · Replies 6 ·
Replies
6

Can Derivatives Exist at Discontinuities of a Piecewise Function?

  • mathmari
  • · Replies 40 ·
2
Replies
40

Graduate Sequence induced by short exact sequence

  • PsychonautQQ
  • · Replies 3 ·
Replies
3

High School Metric for a sphere in polar coordinates

  • Arman777
  • · Replies 11 ·
Replies
11

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

  • member 587159
  • · Replies 4 ·
Replies
4

Undergrad Describing 3d Manifold Objects as a Hypersurface

  • decentMO
  • · Replies 3 ·
Replies
3

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

  • Ethan Singer
  • · Replies 4 ·
Replies
4

Tanh is uniformly continous on R

  • mathmari
  • · Replies 14 ·
Replies
14

Proving Limits of Exponential Series at Infinity

  • mathmari
  • · Replies 7 ·
Replies
7

High School Can three 2-spheres nest cyclically inside each other?

  • Wendel
  • · Replies 8 ·
Replies
8

Orthogonality of vectors in Cauchy-Schwarz proof

  • Math Amateur
  • · Replies 1 ·
Replies
1

Meaning of x^(k) notation in Duistermaat and Kolk lemma 1.1.7

  • Math Amateur
  • · Replies 1 ·
Replies
1

Undergrad Ordered lattice of topologies on the 3 point set

  • jackferry
  • · Replies 1 ·
Replies
1

High School Complex products: perpendicular vectors and rotation effects

  • Ventrella
  • · Replies 3 ·
Replies
3

Find a function so that the composition is continuous

  • mathmari
  • · Replies 20 ·
Replies
20

Undergrad Can We Mathematically Define Everyday Objects Like Smartphones?

  • Tio Barnabe
  • · Replies 21 ·
Replies
21

Show that the function is bounded and strictly increasing

  • mathmari
  • · Replies 12 ·
Replies
12

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

  • mathmari
  • · Replies 14 ·
Replies
14

Why does Conway define completeness for discrete metric spaces?

  • Math Amateur
  • · Replies 4 ·
Replies
4

Evaluate Case of Fresnel Integral

  • Deanmark
  • · Replies 13 ·
Replies
13

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

  • PsychonautQQ
  • · Replies 28 ·
Replies
28

High School How a Klein bottle has a 0 volume?

  • parshyaa
  • · Replies 16 ·
Replies
16

Undergrad Rational sequence converging to irrational

  • Delta2
  • · Replies 13 ·
Replies
13

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

  • mathmari
  • · Replies 8 ·
Replies
8

Finding the Product of Distinct Roots: A Complex Challenge

  • lfdahl
  • · Replies 1 ·
Replies
1

Additional solution for polar form of complex number

  • TheFallen018
  • · Replies 1 ·
Replies
1

Complex Variables - Max Modulus Inequality

  • joypav
  • · Replies 4 ·
Replies
4

Complex Variables - Solution of a System

  • joypav
  • · Replies 3 ·
Replies
3

Adjoint operator and orthogonal projection

  • mathzero
  • · Replies 3 ·
Replies
3

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

  • Jamz
  • · Replies 5 ·
Replies
5

Undergrad Is simulation considered a type of quantitative analysis?

  • Trixie Mattel
  • · Replies 7 ·
Replies
7

Complex Variables - Zeros of Analytic Functions

  • joypav
  • · Replies 4 ·
Replies
4

Complex Variables - Legendre Polynomial

  • joypav
  • · Replies 2 ·
Replies
2

Graduate Torus 2-sheet covering of Klein bottle

  • PsychonautQQ
  • · Replies 22 ·
Replies
22

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

  • DaveC426913
  • · Replies 13 ·
Replies
13

Reconciling Differences in Vector-Valued Function Derivatives

  • Math Amateur
  • · Replies 2 ·
Replies
2

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

  • H Tomasz Grzybowski
  • · Replies 6 ·
Replies
6

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

  • Alone
  • · Replies 7 ·
Replies
7

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

  • PsychonautQQ
  • · Replies 1 ·
Replies
1

Undergrad Cardinality of fibers same for covering maps

  • PsychonautQQ
  • · Replies 17 ·
Replies
17

Undergrad Choosing points from a set that produce the largest polygon

  • Jeff.Nevington
  • · Replies 5 ·
Replies
5

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

  • Adgorn
  • · Replies 45 ·
2
Replies
45

Graduate Fundamental group of a sphere with 6 points removed

  • PsychonautQQ
  • · Replies 15 ·
Replies
15

Directional derivative in scalar fields vs vector fields

  • Math Amateur
  • · Replies 2 ·
Replies
2

How Does Definition 8.9 Imply Differentiability Near Point p?

  • Math Amateur
  • · Replies 1 ·
Replies
1

Proving Browder's proposition 8.12 on vector valued functions

  • Math Amateur
  • · Replies 1 ·
Replies
1

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

  • Math Amateur
  • · Replies 4 ·
Replies
4

Does the Sequence Converge?

  • evinda
  • · Replies 9 ·
Replies
9

Why Does Lemma 8.4 Equal This Expression?

  • Math Amateur
  • · Replies 5 ·
Replies
5

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

  • Math Amateur
  • · Replies 2 ·
Replies
2

Graduate Connected sum of manifolds and free group isomorphisms

  • PsychonautQQ
  • · Replies 15 ·
Replies
15

Why must φ be non-decreasing for γ ∘ φ to preserve trace?

  • Math Amateur
  • · Replies 1 ·
Replies
1

Undergrad Why can we define sequences in this fashion?

  • Oats
  • · Replies 2 ·
Replies
2

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

  • fresh_42
  • · Replies 3 ·
Replies
3

A complex numbers' modulus identity.

  • Alone
  • · Replies 1 ·
Replies
1

Understanding Cantor's Theorem and Diameter

  • Math Amateur
  • · Replies 3 ·
Replies
3

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

  • Math Amateur
  • · Replies 3 ·
Replies
3

Why is sin u ≥ 2u/π for 0 ≤ u ≤ π/2?

  • Math Amateur
  • · Replies 4 ·
Replies
4

Graduate Questions about Covering maps, manifolds, compactness

  • PsychonautQQ
  • · Replies 1 ·
Replies
1

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

  • Math Amateur
  • · Replies 1 ·
Replies
1

Why is Re(z) ≤ |z| in Palka's Lemma 2.1(vi) proof?

  • Math Amateur
  • · Replies 2 ·
Replies
2

Palka lemma 2.1(vi): argument of contour integral and modulus property

  • Math Amateur
  • · Replies 2 ·
Replies
2

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

  • Math Amateur
  • · Replies 2 ·
Replies
2

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

  • Bestfrog
  • · Replies 5 ·
Replies
5

Deriving the simplified expression in Conway's Theorem 2.29

  • Math Amateur
  • · Replies 2 ·
Replies
2

Insights Representations Of The Special Unitary Group SU(2)

  • fresh_42
  • · Replies 3 ·
Replies
3

Complex number geometrical problem

  • amr21
  • · Replies 4 ·
Replies
4

Mapping of a Circle in the Complex Plane

  • amr21
  • · Replies 7 ·
Replies
7

Proof of Divergence: (-1)^n Sequence

  • solakis1
  • · Replies 8 ·
Replies
8

Do we distinguish cases for n?

  • evinda
  • · Replies 12 ·
Replies
12

Analyticity of √(1 + z²) and branch point exclusion in Palka Ch. III

  • Math Amateur
  • · Replies 2 ·
Replies
2

High School Why does √(-i²) give two different answers?

  • Tian En
  • · Replies 6 ·
Replies
6

How Can We Prove the Modified Bernoulli Inequality?

  • evinda
  • · Replies 6 ·
Replies
6

Graduate Fundamental group of n connect tori with one point removed

  • PsychonautQQ
  • · Replies 9 ·
Replies
9

Undergrad Intuition behind induced homomorphism from covering maps

  • PsychonautQQ
  • · Replies 15 ·
Replies
15

Graduate Fundamental group of Project Plane with 2 points missing

  • PsychonautQQ
  • · Replies 6 ·
Replies
6

Lemma 3.1 on disconnected sets in Palka's complex analysis

  • Math Amateur
  • · Replies 2 ·
Replies
2

Limit of e^(-1/z^2) in Palka section 2.2

  • Math Amateur
  • · Replies 2 ·
Replies
2

Palka's limit of complex function with logarithm

  • Math Amateur
  • · Replies 2 ·
Replies
2

Continuity of the argument function in complex plane topology

  • Math Amateur
  • · Replies 2 ·
Replies
2

Undergrad Impossible to lift the identity map on the circle

  • PsychonautQQ
  • · Replies 3 ·
Replies
3

Undergrad Why does the boundary matter for compactness in R²?

  • FallenApple
  • · Replies 12 ·
Replies
12

Undergrad Retract of a connected space is connected

  • PsychonautQQ
  • · Replies 6 ·
Replies
6