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.
Graduate What is the Relationship Between Metrics and Topology?
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad I'm having (another) thick moment (complex numbers)
  • · Replies 5 ·
Replies
5
Views
20K
Graduate Find the proof with supremum for bounded and disjoint sets
  • · Replies 11 ·
Replies
11
Views
9K
Undergrad What is the confusion surrounding complex numbers and their representation?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Cube roots of a complex number
  • · Replies 13 ·
Replies
13
Views
32K
Graduate Questions on functions and supremums and infimums.
  • · Replies 5 ·
Replies
5
Views
7K
Graduate Proving Inequalities Between Infimum and Supremum in Subset Relations
  • · Replies 3 ·
Replies
3
Views
7K
Graduate Geometric Topology Vs. Algebraic Topology.
  • · Replies 1 ·
Replies
1
Views
7K
Undergrad A little help with this complex number question
  • · Replies 6 ·
Replies
6
Views
3K
High School Using complex numbers in polar form on calculator?
  • · Replies 2 ·
Replies
2
Views
9K
Graduate Help with proof for Dirca Delta Relation
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Is Distance an Abstract Concept? A Debate on the Definition of Length
  • · Replies 14 ·
Replies
14
Views
3K
Graduate A world with no curves, artificially creating a circle?
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad Can there be 3 collinear points in a curve?
  • · Replies 25 ·
Replies
25
Views
7K
Graduate Geometry: Learn About Toruses & N-Balls
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad How is the multiplication rule for complex numbers derived?
  • · Replies 11 ·
Replies
11
Views
3K
Graduate What does C^r mean for a function of several variables?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad More on 0.999~ vs 1: Comparing Numbers
  • · Replies 60 ·
3
Replies
60
Views
11K
Undergrad Can All Functions Be Plotted on a Complex Plane?
  • · Replies 1 ·
Replies
1
Views
6K
Undergrad Complex Exponential: Why is e Used?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Elementary Real and Complex Analysis
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Residue of z/cos(z): Explanation & Calculation
  • · Replies 15 ·
Replies
15
Views
17K
Graduate Why are topology and sigma-algebras defined in a similar way?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate What is
  • · Replies 5 ·
Replies
5
Views
11K
Graduate Why Are Only Constant Functions Continuous in Concrete Topology?
  • · Replies 18 ·
Replies
18
Views
6K
Undergrad Help with Describing Image of |z-1| ≤ 1 in Complex Plane
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Complex number exponential subtraction
  • · Replies 4 ·
Replies
4
Views
6K
Graduate What is the Branch of Mathematics that Maps Entire Sub-Disciplines?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Proving Noncompactness of Unit Ball in Infinite-Dimensional Banach Space
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Why is Complex-Number Math Essential in Quantum Physics?
  • · Replies 11 ·
Replies
11
Views
4K
Graduate Unraveling the Topological Equivalence of Vertical and Horizontal Tori
  • · Replies 25 ·
Replies
25
Views
4K
Undergrad Bounded sequence as convergent
  • · Replies 7 ·
Replies
7
Views
21K
Graduate What is the definition of a topological space?
  • · Replies 8 ·
Replies
8
Views
2K
High School What Is Topology: Definition & Examples
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Points in 2- and 3-dimensional space
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Why Does the Equation 1 = -1 Seem Correct?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Complex Numbers & Complex Envelopes: Articles & Resources
  • · Replies 2 ·
Replies
2
Views
3K
Graduate What Makes the Hilbert Cube Cubelike?
  • · Replies 3 ·
Replies
3
Views
4K
Graduate A conjecture about the roots of real functions
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad What do u need to learn topology?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate What is the equivalence of definitions for completely regular spaces?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Visualizing topological spaces
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad 0.999 =1 is LUB or exactly the same
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Complex Numbers: Learn Techniques & De Moivres Theorem
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Complex Plane Dimension Number
  • · Replies 2 ·
Replies
2
Views
3K
Graduate How can complex analysis be applied to Einstein's theory of relativity?
  • · Replies 14 ·
Replies
14
Views
2K
Graduate A question of roots of riemann function
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Importance of Complex Analysis
  • · Replies 25 ·
Replies
25
Views
21K
Graduate Weierstrass approach to analysis
  • · Replies 15 ·
Replies
15
Views
5K
Graduate Explaining topology to non-mathematicians
  • · Replies 44 ·
2
Replies
44
Views
12K
Graduate How Many Roots Exist for Complex Numbers Raised to Irrational Powers?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Trig chart for the complex plane
  • · Replies 22 ·
Replies
22
Views
4K
Graduate Why is (algebraic) topology important?
  • · Replies 3 ·
Replies
3
Views
9K
Graduate Find a root for this expression:
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Laurent series of the function f(z)=1/z^2 for |z-a|>|a|
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Calculate sin and cos using complex numbers
  • · Replies 12 ·
Replies
12
Views
11K
Graduate Complex numbers and modulus problem
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad What are Möbius Transformations and What are Their Applications?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad How to Express a Complex Number in the Form of I-Tan(kA)?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate No Complex Analysis Equation z^4 + z + 5 = 0
  • · Replies 13 ·
Replies
13
Views
3K
Graduate Van Kampen's theorem and fundamental groups
  • · Replies 7 ·
Replies
7
Views
8K
Graduate What values of z in the complex plane make the series absolutely convergent?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate What is the Mystery Behind i^i? Unveiling the Intricacies of Euler's Formula
  • · Replies 19 ·
Replies
19
Views
5K
Graduate Uniform Metric vs Box Topology
  • · Replies 2 ·
Replies
2
Views
8K
Graduate Can Complex Analysis Solve x^{sin(y)}=y^{cos(x)}?
  • · Replies 11 ·
Replies
11
Views
3K
Graduate What is the definition of 'space'?
  • · Replies 4 ·
Replies
4
Views
6K
Graduate Compact sets and homeomorphisms
  • · Replies 24 ·
Replies
24
Views
10K
High School Understanding Imaginary Roots in Complex Numbers
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Conformal mapping in Complex Analysis
  • · Replies 5 ·
Replies
5
Views
14K
Undergrad Complex numbers and coordinates
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Finding Flaw in Reasoning: Complex Fun
  • · Replies 12 ·
Replies
12
Views
2K
Graduate What is the basis for the inner product of functions?
  • · Replies 2 ·
Replies
2
Views
15K
High School Solving Complex Polynomial Equations
  • · Replies 9 ·
Replies
9
Views
4K
Graduate Relative Boundaries in General Topology
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Can You Create a Bijective Function from the Reals to the Interval [0,1]?
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad (x)=max{f(x),g(x)} continuous functions
  • · Replies 4 ·
Replies
4
Views
10K
Graduate Complex Analysis: Applications & Virtual Classrooms
  • · Replies 6 ·
Replies
6
Views
4K
Undergrad What is the definition of distance between a point and a set of points?
  • · Replies 4 ·
Replies
4
Views
12K
Graduate Contour Integration: Find Out Non-Removable Singularities?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Solving Ln(-1) with Euler's Equation
  • · Replies 12 ·
Replies
12
Views
3K
Graduate Has the Poincaré Conjecture Been Proven? A Review of the Proposed Proof
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Sequence of rationals that converge to irrational
  • · Replies 10 ·
Replies
10
Views
28K
Graduate A Question About the Complex Plane
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Is .999' Equal to 1? A Proof Using Reductio Ad Absurdum
  • · Replies 13 ·
Replies
13
Views
5K
Undergrad Is the Function f(x) Continuous at x=0 Given Its Definition and Behavior?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Accumulation/densification points.
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How can I express the coordinates of a pentagram in the complex plane using Phi?
  • · Replies 6 ·
Replies
6
Views
6K
Graduate Mean ergodic theorem von Neumann
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Can A Three-String Knot be Constructed?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate What is the Completeness Axiom?
  • · Replies 12 ·
Replies
12
Views
12K
Undergrad Is There Always a Real Number Between Two Arbitrary Real Numbers?
  • · Replies 3 ·
Replies
3
Views
3K
High School Can someone please explain to me what topology is?
  • · Replies 21 ·
Replies
21
Views
4K
High School What Are the Best Sources and Theories on Complex Numbers?
  • · Replies 18 ·
Replies
18
Views
4K
Undergrad Can someone explain the property of complex conjugates in this equation?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate What is the theory behind analytical continuations?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How Can You Explore Solutions for ln() with Negative Values?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad What are the solutions for ln(z) = -1?
  • · Replies 19 ·
Replies
19
Views
12K
Graduate De Branges and the Riemann Hypothesis
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Aysmptotics : Need help with residues
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad What is the real part of a function like f(z)= √(z)?
  • · Replies 7 ·
Replies
7
Views
13K