Topology and Analysis Forum

Post thread
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.
I Why can we define sequences in this fashion?
  • · Replies 2 ·
Replies
2
Views
2K
Insights The Different Faces Of The Special Unitary Group ##SU(2)##
  • · Replies 3 ·
Replies
3
Views
2K
MHB Understanding Cantor's Theorem and Diameter
  • · Replies 3 ·
Replies
3
Views
2K
MHB Complex Valued Functions BV: John B. Conway Prop 1.3 Explained
  • · Replies 3 ·
Replies
3
Views
2K
MHB Contour Integrals - Example 2.5, Palka, Section 2.2, Ch.4 .... ....
  • · Replies 4 ·
Replies
4
Views
2K
A Questions about Covering maps, manifolds, compactness
  • · Replies 1 ·
Replies
1
Views
2K
MHB Understand Proposition 1.3 in Conway's Functions of Complex Variables I
  • · Replies 1 ·
Replies
1
Views
2K
MHB Proof of Lemma 2.1, Part (vi) in Palka's Ch.4: Explaining Inequality
  • · Replies 2 ·
Replies
2
Views
1K
MHB Properties of Contour Integrals - Palka Lemma 2.1 (vi) .... ....
  • · Replies 2 ·
Replies
2
Views
1K
MHB How Can \dot{\gamma}(0) Fail to Exist in Palka's Example 1.3?
  • · Replies 2 ·
Replies
2
Views
2K
I Where can I find a proof of the Swiss cheese theorem?
  • · Replies 5 ·
Replies
5
Views
3K
MHB How does Conway's Theorem 2.29 Derive the Simplified Expression for f(z)?
  • · Replies 2 ·
Replies
2
Views
2K
Insights Representations Of The Special Unitary Group SU(2)
  • · Replies 3 ·
Replies
3
Views
2K
MHB Complex number geometrical problem
  • · Replies 4 ·
Replies
4
Views
2K
MHB Do we distinguish cases for n?
  • · Replies 12 ·
Replies
12
Views
3K
MHB Analytic Functions - Palka, Ch. III, Section 1.3 ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB How Can We Prove the Modified Bernoulli Inequality?
  • · Replies 6 ·
Replies
6
Views
2K
A Fundamental group of n connect tori with one point removed
  • · Replies 9 ·
Replies
9
Views
4K
I Intuition behind induced homomorphism from covering maps
  • · Replies 15 ·
Replies
15
Views
3K
A Fundamental group of Project Plane with 2 points missing
  • · Replies 6 ·
Replies
6
Views
4K
MHB Disconnected Sets .... Palka, Lemma 3.1 ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB Limits of Complex Functions .... Final Remark from Palka in Section 2.2 ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB Limits of Complex Functions .... Example from Palka ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB Continuity of Complex Functions .... ....
  • · Replies 2 ·
Replies
2
Views
2K
I Impossible to lift the identity map on the circle
  • · Replies 3 ·
Replies
3
Views
2K
I Understanding Compactness in ##R^2##: Analyzing Boundaries and Open Disks
  • · Replies 12 ·
Replies
12
Views
2K
I Retract of a connected space is connected
  • · Replies 6 ·
Replies
6
Views
2K
I Proof that retract of Hausdorff space is closed
  • · Replies 1 ·
Replies
1
Views
4K
I How Does Closure in a Neighborhood Imply Membership in a Set?
  • · Replies 12 ·
Replies
12
Views
2K
MHB The Residue Theorem To Evaluate Integrals
  • · Replies 5 ·
Replies
5
Views
2K
I Is S^2 - {N} Homeomorphic to R^2?
  • · Replies 3 ·
Replies
3
Views
3K
MHB Using Residue Theorem To Prove Value Of Summation
  • · Replies 4 ·
Replies
4
Views
2K
I Euler Characteristic of the Projective plane and sphere?
  • · Replies 3 ·
Replies
3
Views
3K
I What is an atlas for a torus manifold?
  • · Replies 4 ·
Replies
4
Views
8K
MHB Theorem 1.8: Sets or Domains in the Complex Plane - Palka Ch.2
  • · Replies 3 ·
Replies
3
Views
2K
MHB Why Does γ(t) = z(1-t) Represent the Same Curve in Reverse?
  • · Replies 1 ·
Replies
1
Views
2K
I Homotopy Class vs Fundamental Group.
  • · Replies 6 ·
Replies
6
Views
3K
A Is the Long Line Locally Euclidean, Hausdorff, and Path Connected?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Another Question On B&S, Theorem 7.3.5 - Fundamental Theorem Of Calculus ...
  • · Replies 2 ·
Replies
2
Views
2K
MHB Fundamental Theorem Of Calculus (Second Form) - B&S Theorem 7.3.5 .... ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB Convergence in topological space
  • · Replies 2 ·
Replies
2
Views
2K
MHB Riemann Integration - The Additivity Theorem .... B&S Theorem 7.2.9 ....
  • · Replies 1 ·
Replies
1
Views
2K
MHB Limit Superior .... B&S Therem 3.4.11 .... ....
  • · Replies 5 ·
Replies
5
Views
2K
I Proving Convergence: Solving the Limit of 1/(6n^2+1) = 0
  • · Replies 8 ·
Replies
8
Views
2K
I How can we characterize mathematical analysis?
  • · Replies 2 ·
Replies
2
Views
1K
I How Does the Supremum of -A Relate to Its Elements?
  • · Replies 5 ·
Replies
5
Views
1K
MHB Remarks on Limit Superrior .... B&S Page 82 .... Example ....
  • · Replies 2 ·
Replies
2
Views
1K
A Hahn-Banach From Systems of Linear Equations
  • · Replies 9 ·
Replies
9
Views
2K
I Proving that square root of 2 exists
  • · Replies 16 ·
Replies
16
Views
3K
I Irreducible representation of SU(2)
  • · Replies 3 ·
Replies
3
Views
2K
I Noncompact locally compact Hausdorff continuous mapping
  • · Replies 14 ·
Replies
14
Views
2K
I Continuity of the determinant function
  • · Replies 1 ·
Replies
1
Views
7K
I Can a Topological Space be Both a 1-Manifold and an n-Manifold?
  • · Replies 17 ·
Replies
17
Views
3K
I Generalization of measure theory to uncountable unions
  • · Replies 5 ·
Replies
5
Views
2K
MHB L'Hospital's Rule .... Bartle and Sherbert Theorem 6.2.3 .... ....
  • · Replies 3 ·
Replies
3
Views
2K
MHB What is the connection between sin and cos in Example 6.3.4?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Understanding Corollary 6.2.2 of B&S Theorem 6.2.1
  • · Replies 8 ·
Replies
8
Views
4K
I Corollary to the Interior Extremum Theorem .... ....
  • · Replies 3 ·
Replies
3
Views
4K
I Is e: [0,1] --> S^1 a Quotient Map?
  • · Replies 3 ·
Replies
3
Views
2K
I Does L_g pass to the quotient G/H?
  • · Replies 4 ·
Replies
4
Views
2K
I What Is a Non-Linear Ordered Set?
  • · Replies 1 ·
Replies
1
Views
1K
I Is R_d x R Locally Euclidean of Dimension 1?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Chain Rule - B&S Theorem 6.1.6 ....
  • · Replies 3 ·
Replies
3
Views
2K
I Gluing lemma / infinite corollary
  • · Replies 6 ·
Replies
6
Views
3K
I Contort rectangle to torus minus splice=homomorphism?
  • · Replies 1 ·
Replies
1
Views
1K
I Why is this line not homeomorphic to the unit circle?
  • · Replies 10 ·
Replies
10
Views
6K
I Limits and Continuity - Absolute Value Technicality ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB Lipschitz Condition and Uniform Continuity
  • · Replies 1 ·
Replies
1
Views
2K
I Relation of completeness to the l.u.b. property?
  • · Replies 5 ·
Replies
5
Views
2K
MHB Continuous Functions on Intervals .... B&S Theorem 5.3.2 ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB Continuous Functions - Thomae's Function ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB Proving the Sum of a Sequence Equals n Using Induction
  • · Replies 6 ·
Replies
6
Views
2K
I Pole in Stereographic Projection
  • · Replies 1 ·
Replies
1
Views
1K
A Algebraic topology applied to Neuroscience
  • · Replies 2 ·
Replies
2
Views
4K
MHB Limits of Functions .... L&S Example 10.7 (2) ....
  • · Replies 3 ·
Replies
3
Views
1K
MHB Limits of Functions .... B&S Theorem 4.2.9 .... ....
  • · Replies 2 ·
Replies
2
Views
2K
B Understanding Extremum and Derivatives at Boundary Points
  • · Replies 4 ·
Replies
4
Views
2K
B Graphical Representation of a Complex Sphere
  • · Replies 6 ·
Replies
6
Views
2K
I Simplicial complex geometric realization 1-manifold
  • · Replies 2 ·
Replies
2
Views
2K
MHB Limits and Continuity - Absolute Value Technicality ....
  • · Replies 3 ·
Replies
3
Views
1K
B Does Every Set in the Axiom of Choice Include an Empty Set?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Limits of Sequences .... Bartle and Shebert, Example 3.4.3 (b) ....
  • · Replies 6 ·
Replies
6
Views
2K
MHB Limits of Sequences .... Stoll Theorem 2.2.6
  • · Replies 4 ·
Replies
4
Views
2K
MHB Ordering on the Set of Real Numbers .... Sohrab, Exercise 2.1.10 (1) ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB Ordering on the Set of Real Numbers .... Sohrab, Exercise 2.1.12 ....
  • · Replies 2 ·
Replies
2
Views
1K
MHB Ordering on the Set of Real Numbers .... Sohrab, Exercise 2.1.10 (b) ....
  • · Replies 5 ·
Replies
5
Views
2K
MHB Ordering on the Set of Real Numbers .... Sohrab, Exercise 2.1.10 (c) ....
  • · Replies 3 ·
Replies
3
Views
2K
I Limits of Sequences .... Bartle & Shebert, Example 3.4.3 (b)
  • · Replies 3 ·
Replies
3
Views
2K
I Ascending subset sequence with axiom of choice
  • · Replies 3 ·
Replies
3
Views
2K
MHB Open Sets - Unions and Intersections -
  • · Replies 8 ·
Replies
8
Views
2K
MHB Limits of Sequences .... Sohrab Exercise 2.2.7
  • · Replies 3 ·
Replies
3
Views
2K
MHB Closed Sets - Sohrab Exercise 2.2.4 - Part 2
  • · Replies 3 ·
Replies
3
Views
1K
MHB Open and Closed Sets - Sohrab Exercise 2.4.4 - Part 3
  • · Replies 2 ·
Replies
2
Views
2K
MHB Supremum Property (AoC) .... etc .... Yet a further question/Issue ....
  • · Replies 2 ·
Replies
2
Views
1K
MHB Supremum Property (AoC) .... etc .... Another question/Issue ....
  • · Replies 2 ·
Replies
2
Views
1K
MHB Supremum Property (AoC), Archimedean Property, Nested Intervals Theorem ....
  • · Replies 2 ·
Replies
2
Views
2K
I Hyperreal Convergence: Is It 0 or Infinitesimal?
  • · Replies 1 ·
Replies
1
Views
2K
I Supremum Property (AoC) .... etc .... Yet a further question
  • · Replies 3 ·
Replies
3
Views
2K
I Why Does the Cut of $\mathbb{Q}$ Correspond to $\sqrt{2}$?
  • · Replies 3 ·
Replies
3
Views
1K
I Supremum Property, Archimedean Property, Nested Intervals
  • · Replies 4 ·
Replies
4
Views
4K