Topology and Analysis Forum

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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.
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Insights A Path to Fractional Integral Representations of Some Special Functions
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I On integral of simple function and representation
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I Collection of finite unions of half-open intervals form an algebra
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I Parallel rectangles contained in oblique rectangle
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I Help with basic transfinite induction proof
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I On two definitions of locally compact
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I Foliation of the 3-torus
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I Two basic results from measure theory -- on volumes of rectangles
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I In which sense(s) do square integrable functions go to zero at infinity?
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A Functional Analysis for Physics in 2024
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I Question about branch of logarithms
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I Verify the completion of continuous compactly supported functions
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I Showing equivalence of two definitions of essential supremum
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I On deriving the (inverse) Fourier transform from Fourier series
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I "Magic" regulating functions for divergent series
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I Fiber bundle homeomorphism with the fiber
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I Regarding Wirtinger's inequality
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I ##SU(2, \mathbb C)## parametrization using Euler angles
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I ##SL(2,\mathbb R)## Lie group as manifold
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I Homeomorphism linear subspace
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I ##SU(2)## homeomorphic with ##\mathbb S^3##
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I New Video Course on General Topology on YouTube
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I How do I use the four axioms of a neighborhood to define an open set?
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I How to define an open set using the four axioms of a neighborhood
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I Bloch Analysis proof of Theorem 2.5.5 (Definition by recursion)
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I Is the Belt Trick Possible with Continuous Deformation in 3D Rotation Space?
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A Complex analysis -- Essential singularity
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I On differentiability and Fourier coefficients (Vretblad's text)
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I On limit of convolution of function with a summability kernel
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I Fourier coefficients of convolution
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I Bounding modulus of complex logarithm times complex power function
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B Confusion with the basics of Topology (Poincare conjecture)
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I On a remark regarding the Cauchy integral formula
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B Questions on a numberphile video
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I Topological argument principle
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I Infinity Numbers (Expanded P-Adic Numbers)
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I Why is this function not ##L^1(\mathbb{R} \times \mathbb{R})##?
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I Prove projection of a measurable set from product space is measurable
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B Why is the set {(x,y)∈Ω×R|y=f(x)} a manifold?
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A Topology - Boundary of a ball without a point
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I Feedback for my YouTube Videos on Real Analysis
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I Using Residues (Complex Analysis) to compute partial fractions
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I Is the Set of Integer Outputs of sin(x) Sequentially Compact in ℝ?
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B Understanding Dedekind Cuts: Exploring Addition and Negative Numbers
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I Circuits or edge-disjoint unions of circuits in a connected graph
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I Calculate the residue of 1/Cosh(pi.z) at z = i/2 (complex analysis)
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B Mapping wave forms to sphere, does wave form y=0 have a reflection?
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I Can you somehow make left handed helix into a right handed?
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A Regarding fibrations between smooth manifolds
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B Aperiodic Tiling with a single tile shape
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I Geometry of series terms of the Riemann Zeta Function
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I Upper and Lower Darboux Sum Inequality
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A Infinite series of this type converges?
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I In a 3-dimension isoperimetric problem, a ball maximizes the volume
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I Original definition of Riemann Integral and Darboux Sums
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I Create a surjective function from [0,1]^n→S^n
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I Lars Olsen proof of Darboux's Intermediate Value Theorem for Derivatives
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A Norm 2, f Integrable function, show: ##||f-g||_2<\epsilon##
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I Does topology distinguish between real and imaginary dimensions?
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I Understanding an argument in Intermediate Value Theorem
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I Are there any elementary functions of norms that are still norms?
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I Applications of measurement of commutativity
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B Is the Texan Conjecture a mathematical truth or a myth?
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I If a sequence converges, then all subsequences of it have same limit
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I I would like opinions of the latest draft of my note - Integration
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I Discrete Subrings of Complex Numbers: Topology of Rings
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A PD code yields two different knot diagrams
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MHB Sobolev space H^2(0,1) and H^3(0,1)
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A Laurent series for algebraic functions
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I How can I use the concept of a proper map to show that a set is bounded?
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A What does the metric of a 6D space with 3 compactified dimensions look like?
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I ##\epsilon - \delta## proof and algebraic proof of limits
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I The asymptotic behaviour of Elliptic integral near k=1
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I I need integrals Int[0,infty]t^(a-1) e^(-t) F(z, e^(-t))dt
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I Functions.wolfram.com accepted and published my formula for Gamma Fn
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MHB Outer measure .... Axler, Result 2.8 ....
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I Proving a convergent sequence is bounded
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I Fourier transform of a beat
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I Proof of Induction Principle starting from N, not from 1
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I Looking for an expert on integrals
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A Confused by a theorem in Milnor-Stasheff
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I Looking for Someone Strong in Analysis
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MHB Proving Lemma 3.3 of L&S: Further Aspects of the Proof
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MHB An Aspect of Lemma 3.3 .... Laczkovich and Vera T Sos .... L&S ....
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MHB Checking Proof of Theorem 6.2.8 Part (ii)
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MHB How can we prove the inequality for the supremum and infimum of f*g and f*g?
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MHB Infinite series involving 'x' has a constant value
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MHB Understanding Riemann Integrable Functions: Interpreting D&K Pages 427-428
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MHB Recursive Function for Virus Spread: Finding the General Solution
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MHB Exploring Proposition 6.1.2 from D&K's Multidimensional Real Analysis II (Integration)
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MHB Help Needed with Determining B' in Proposition 6.1.2: A Case for n=2
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I In Euclidian space, closed ball is equal to closure of open ball
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I Duistermaat & Kolk .... Vol II .... Proof of Proposition 6.1.2
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MHB Duistermaat & Kolk .... Vol II .... Proposition 6.1.2
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A Understanding Cantor set C in Ternary form with 1/n factor in front C
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I A curve that does not meet rational points
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I Simpler Brunnian "rubberband" loops?
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I Writing down an explicit homotopy
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I Understanding the Role of the Identity Map in Fundamental Group Theory
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I Describing homeomorphisms with the π1 function
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I What's the definition of "periodic extension of a function"?
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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.
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