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.
  • Sticky
Insights A Path to Fractional Integral Representations of Some Special Functions
Replies
9
Views
5K
I Are slices of measurable functions measurable?
Replies
2
Views
39
I On integral of simple function and representation
Replies
6
Views
350
I Parallel rectangles contained in oblique rectangle
Replies
3
Views
189
I Collection of finite unions of half-open intervals form an algebra
Replies
3
Views
232
I Foliation of the 3-torus
Replies
8
Views
307
I Help with basic transfinite induction proof
Replies
2
Views
170
I On two definitions of locally compact
Replies
5
Views
225
I Showing equivalence of two definitions of essential supremum
Replies
1
Views
210
I Two basic results from measure theory -- on volumes of rectangles
Replies
2
Views
147
I In which sense(s) do square integrable functions go to zero at infinity?
Replies
2
Views
164
A Functional Analysis for Physics in 2024
Replies
11
Views
273
I Question about branch of logarithms
Replies
14
Views
478
I Verify the completion of continuous compactly supported functions
Replies
4
Views
352
I Fiber bundle homeomorphism with the fiber
2
Replies
43
Views
980
I On deriving the (inverse) Fourier transform from Fourier series
Replies
4
Views
312
I Prove projection of a measurable set from product space is measurable
Replies
3
Views
1K
B Questions on a numberphile video
Replies
5
Views
891
I "Magic" regulating functions for divergent series
Replies
0
Views
211
I ##SU(2, \mathbb C)## parametrization using Euler angles
Replies
16
Views
538
I Regarding Wirtinger's inequality
Replies
4
Views
285
I ##SL(2,\mathbb R)## Lie group as manifold
Replies
12
Views
388
I Is the Projection Restriction to a Linear Subspace a Homeomorphism?
Replies
8
Views
483
I New Video Course on General Topology on YouTube
Replies
2
Views
379
I ##SU(2)## homeomorphic with ##\mathbb S^3##
2
Replies
61
Views
1K
I Bloch Analysis proof of Theorem 2.5.5 (Definition by recursion)
Replies
2
Views
339
I How do I use the four axioms of a neighborhood to define an open set?
Replies
2
Views
332
I How to define an open set using the four axioms of a neighborhood
Replies
2
Views
359
I Is the Belt Trick Possible with Continuous Deformation in 3D Rotation Space?
Replies
8
Views
634
I On differentiability and Fourier coefficients (Vretblad's text)
Replies
4
Views
382
A Complex analysis -- Essential singularity
Replies
6
Views
376
I On limit of convolution of function with a summability kernel
Replies
2
Views
401
I Fourier coefficients of convolution
Replies
1
Views
418
I Outer measure .... Axler, Result 2.14 .... Another Question ....
Replies
8
Views
2K
I Bounding modulus of complex logarithm times complex power function
Replies
4
Views
761
B Confusion with the basics of Topology (Poincare conjecture)
Replies
2
Views
691
I Topological argument principle
Replies
8
Views
959
I On a remark regarding the Cauchy integral formula
Replies
2
Views
649
I Infinity Numbers (Expanded P-Adic Numbers)
Replies
10
Views
1K
I Why is this function not ##L^1(\mathbb{R} \times \mathbb{R})##?
Replies
6
Views
865
B Why is the set {(x,y)∈Ω×R|y=f(x)} a manifold?
Replies
6
Views
928
A Topology - Boundary of a ball without a point
Replies
5
Views
1K
I Feedback for my YouTube Videos on Real Analysis
Replies
4
Views
982
B Understanding Dedekind Cuts: Exploring Addition and Negative Numbers
Replies
6
Views
1K
I Using Residues (Complex Analysis) to compute partial fractions
Replies
4
Views
1K
I Is the Set of Integer Outputs of sin(x) Sequentially Compact in ℝ?
Replies
3
Views
861
I Circuits or edge-disjoint unions of circuits in a connected graph
Replies
1
Views
799
I Can you somehow make left handed helix into a right handed?
Replies
8
Views
1K
MHB Outer measure .... Axler, Result 2.8 ....
Replies
2
Views
1K
I Calculate the residue of 1/Cosh(pi.z) at z = i/2 (complex analysis)
Replies
7
Views
1K
B Mapping wave forms to sphere, does wave form y=0 have a reflection?
Replies
3
Views
929
B Aperiodic Tiling with a single tile shape
Replies
5
Views
1K
A Regarding fibrations between smooth manifolds
Replies
1
Views
787
I Geometry of series terms of the Riemann Zeta Function
Replies
3
Views
1K
I I need a mapping from the unit Hypercube [0,1]^n to a given simplex
Replies
17
Views
3K
I Discrete Subrings of Complex Numbers: Topology of Rings
Replies
11
Views
1K
MHB Checking Proof of Theorem 6.2.8 Part (ii)
Replies
2
Views
2K
I I would like opinions of the latest draft of my note - Integration
Replies
4
Views
1K
I Upper and Lower Darboux Sum Inequality
Replies
2
Views
914
I Original definition of Riemann Integral and Darboux Sums
Replies
14
Views
2K
MHB Exploring Proposition 6.1.2 from D&K's Multidimensional Real Analysis II (Integration)
Replies
2
Views
2K
A Infinite series of this type converges?
Replies
5
Views
954
I In a 3-dimension isoperimetric problem, a ball maximizes the volume
Replies
6
Views
1K
I A curve that does not meet rational points
Replies
2
Views
1K
I Create a surjective function from [0,1]^n→S^n
Replies
8
Views
1K
I Lars Olsen proof of Darboux's Intermediate Value Theorem for Derivatives
Replies
9
Views
1K
A Norm 2, f Integrable function, show: ##||f-g||_2<\epsilon##
Replies
5
Views
1K
I Does topology distinguish between real and imaginary dimensions?
2
Replies
35
Views
2K
I Understanding the Role of the Identity Map in Fundamental Group Theory
Replies
2
Views
1K
MHB How to Prove a Complex Number Equation and Its Trajectory Forms a Circle?
Replies
2
Views
2K
I Understanding an argument in Intermediate Value Theorem
Replies
5
Views
1K
I Are there any elementary functions of norms that are still norms?
Replies
4
Views
1K
I Applications of measurement of commutativity
Replies
5
Views
1K
MHB A forgotten L-Transform formula
Replies
2
Views
2K
Is the Integral Inequality Possible to Prove for Certain Parameters?
Replies
2
Views
3K
A Ref: "Standard" Action of S^1 on S^n ?
2
Replies
64
Views
7K
B Is the Texan Conjecture a mathematical truth or a myth?
Replies
5
Views
1K
MHB The Supremum of a Set is not an Interior Point
Replies
2
Views
2K
I If a sequence converges, then all subsequences of it have same limit
Replies
7
Views
2K
MHB How Can I Tackle Difficult Questions Effectively?
Replies
2
Views
1K
A Laurent series for algebraic functions
Replies
9
Views
2K
MHB Proving Measure Space Properties of $(X,\bar{\mathcal{B}} ,\bar{\mu})$
Replies
2
Views
1K
A PD code yields two different knot diagrams
Replies
3
Views
1K
MHB Sobolev space H^2(0,1) and H^3(0,1)
Replies
1
Views
1K
I How can I use the concept of a proper map to show that a set is bounded?
Replies
18
Views
2K
I ##\epsilon - \delta## proof and algebraic proof of limits
2
Replies
48
Views
3K
MHB Prove that the function is monotonic and not decreasing
Replies
2
Views
1K
B Is the 10 Dimensional Poincaré Group a Coincidence?
Replies
2
Views
1K
A What does the metric of a 6D space with 3 compactified dimensions look like?
Replies
20
Views
2K
I The asymptotic behaviour of Elliptic integral near k=1
Replies
2
Views
1K
I I need integrals Int[0,infty]t^(a-1) e^(-t) F(z, e^(-t))dt
Replies
4
Views
1K
MHB Proving Relatively Compactness in C([a, b]) using Arzelá-Ascoli Theorem
Replies
2
Views
1K
MHB Prove that it converges uniformly
Replies
2
Views
1K
I Functions.wolfram.com accepted and published my formula for Gamma Fn
Replies
11
Views
1K
I Proving a convergent sequence is bounded
Replies
3
Views
1K
I How Does Fourier Transform Analyze Beats in Signals?
Replies
7
Views
2K
I Proof of Induction Principle starting from N, not from 1
Replies
6
Views
1K
I Looking for an expert on integrals
Replies
1
Views
1K
MHB Discover the Limit of a Sequence with Easy-to-Follow Steps
Replies
2
Views
1K
A Confused by a theorem in Milnor-Stasheff
Replies
4
Views
1K
MHB How Do Riemann Integrals Handle Function Splits and Summations?
Replies
2
Views
1K

Hot Threads

Recent Insights

Topology and Analysis

Welcome to the Topology forum!

Topology and analysis are two branches of mathematics that investigate the properties of spaces and functions, respectively. Topology is concerned with the study of the properties that remain unchanged under continuous deformations, such as stretching or bending, but not tearing. It explores concepts like continuity, connectedness, and compactness.

Analysis, on the other hand, is focused on understanding the behavior of mathematical functions and sequences. It deals with limits, continuity, differentiation, and integration, providing tools for a detailed examination of functions. Both topology and analysis play integral roles in diverse areas of mathematics and find applications in various scientific and engineering disciplines.

Together, they contribute to a deeper understanding of the structure and properties of mathematical objects.
Back
Top