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
6K
I Exercise 2.23 in Folland's real analysis text
Replies
1
Views
42
I 3-sphere with Ricci flow
Replies
0
Views
74
I Regarding dominated convergence theorem in Folland
Replies
5
Views
135
I On Borel sets of the extended reals
Replies
2
Views
438
I Basic question on 'bounded implies totally bounded'
Replies
16
Views
364
I Open balls dense in closed balls in Euclidean space
Replies
2
Views
260
I Show that a "cross" is not a topological manifold
Replies
20
Views
679
I Tough lemma on locally finite refinement
Replies
8
Views
449
A Cubical cup poduct with a unit 1-cochain and the coboundary operator
Replies
0
Views
192
I Compact support functions and law of a random variable
Replies
11
Views
524
I Uniform closure of algebra of bounded functions is uniformly closed
Replies
2
Views
353
I Parallel rectangles contained in oblique rectangle
Replies
5
Views
1K
A Question about different statements of Picard Theorem
Replies
0
Views
495
I Question about convex property in Jensen's inequality
Replies
4
Views
422
I A non-empty intersection of closures of level sets implies discontinuity
Replies
1
Views
511
A Proving that this integral is divergent
Replies
2
Views
560
A Question about covering map of punctured unit disk
Replies
3
Views
438
A Question about lifting of a function
Replies
2
Views
569
A Question about existence of path-lifting property
Replies
8
Views
552
I Riemann integrability and uniform convergence
Replies
2
Views
912
MHB Integration in Polar Coordinates (Fubini/Tonelli)
Replies
4
Views
2K
I On theorem 1.19 in Folland's and completion of measure
Replies
1
Views
749
I Are slices of measurable functions measurable?
Replies
3
Views
691
I On integral of simple function and representation
Replies
6
Views
898
I Collection of finite unions of half-open intervals form an algebra
Replies
3
Views
863
I Foliation of the 3-torus
Replies
8
Views
855
I Help with basic transfinite induction proof
Replies
2
Views
702
I On two definitions of locally compact
Replies
5
Views
866
I Showing equivalence of two definitions of essential supremum
Replies
1
Views
692
I Two basic results from measure theory -- on volumes of rectangles
Replies
2
Views
639
I In which sense(s) do square integrable functions go to zero at infinity?
Replies
2
Views
759
A Functional Analysis for Physics in 2024
Replies
11
Views
754
I Question about branch of logarithms
Replies
14
Views
1K
I Verify the completion of continuous compactly supported functions
Replies
4
Views
835
I Fiber bundle homeomorphism with the fiber
2
Replies
43
Views
2K
I On deriving the (inverse) Fourier transform from Fourier series
Replies
4
Views
978
I Prove projection of a measurable set from product space is measurable
Replies
3
Views
2K
B Questions on a numberphile video
Replies
5
Views
1K
I "Magic" regulating functions for divergent series
Replies
0
Views
621
I ##SU(2, \mathbb C)## parametrization using Euler angles
Replies
16
Views
1K
I Regarding Wirtinger's inequality
Replies
4
Views
904
I ##SL(2,\mathbb R)## Lie group as manifold
Replies
12
Views
924
I Is the Projection Restriction to a Linear Subspace a Homeomorphism?
Replies
8
Views
1K
I New Video Course on General Topology on YouTube
Replies
2
Views
947
I ##SU(2)## homeomorphic with ##\mathbb S^3##
2
Replies
61
Views
2K
I Bloch Analysis proof of Theorem 2.5.5 (Definition by recursion)
Replies
2
Views
835
I How do I use the four axioms of a neighborhood to define an open set?
Replies
2
Views
766
I How to define an open set using the four axioms of a neighborhood
Replies
2
Views
816
I Is the Belt Trick Possible with Continuous Deformation in 3D Rotation Space?
Replies
8
Views
1K
I On differentiability and Fourier coefficients (Vretblad's text)
Replies
4
Views
906
A Complex analysis -- Essential singularity
Replies
6
Views
865
I On limit of convolution of function with a summability kernel
Replies
2
Views
923
I Fourier coefficients of convolution
Replies
1
Views
916
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
1K
B Confusion with the basics of Topology (Poincare conjecture)
Replies
2
Views
1K
I Is a Locally One-to-One Proper Map Globally Bijective?
Replies
8
Views
1K
I On a remark regarding the Cauchy integral formula
Replies
2
Views
1K
I Infinity Numbers (Expanded P-Adic Numbers)
Replies
10
Views
2K
I Why is this function not ##L^1(\mathbb{R} \times \mathbb{R})##?
Replies
6
Views
1K
B Why is the set {(x,y)∈Ω×R|y=f(x)} a manifold?
Replies
6
Views
1K
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
1K
B Understanding Dedekind Cuts: Exploring Addition and Negative Numbers
Replies
6
Views
2K
I Using Residues (Complex Analysis) to compute partial fractions
Replies
4
Views
2K
I Is the Set of Integer Outputs of sin(x) Sequentially Compact in ℝ?
Replies
3
Views
1K
I Circuits or edge-disjoint unions of circuits in a connected graph
Replies
1
Views
1K
I Can you somehow make left handed helix into a right handed?
Replies
8
Views
2K
MHB Outer measure .... Axler, Result 2.8 ....
Replies
2
Views
2K
I Calculate the residue of 1/Cosh(pi.z) at z = i/2 (complex analysis)
Replies
7
Views
2K
B Mapping wave forms to sphere, does wave form y=0 have a reflection?
Replies
3
Views
1K
B Aperiodic Tiling with a single tile shape
Replies
5
Views
2K
A Regarding fibrations between smooth manifolds
Replies
1
Views
1K
I Geometry of series terms of the Riemann Zeta Function
Replies
3
Views
2K
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
2K
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
2K
I Upper and Lower Darboux Sum Inequality
Replies
2
Views
1K
I Original definition of Riemann Integral and Darboux Sums
Replies
14
Views
2K
MHB How to Prove \(\text{vol}_n (B) = \text{vol}_n (B') + \text{vol}_n (B'')\)?
Replies
2
Views
3K
A Infinite series of this type converges?
Replies
5
Views
1K
I In a 3-dimension isoperimetric problem, a ball maximizes the volume
Replies
6
Views
2K
I A curve that does not meet rational points
Replies
2
Views
2K
I Create a surjective function from [0,1]^n→S^n
Replies
8
Views
2K
I Lars Olsen proof of Darboux's Intermediate Value Theorem for Derivatives
Replies
9
Views
2K
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
3K
I Understanding the Role of the Identity Map in Fundamental Group Theory
Replies
2
Views
2K
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
2K
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 Can This Forgotten Formula Simplify the Laplace Transform of \(y(t)^3\)?
Replies
2
Views
3K
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
9K
B Is the Texan Conjecture a mathematical truth or a myth?
Replies
5
Views
2K
MHB The Supremum of a Set is not an Interior Point
Replies
2
Views
3K
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
2K

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