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.
MHB Properties of Riemann Integrable Functions with Compact Support .... Proof of D&K Theorem 6.2.8 ....
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MHB Help Needed with Determining B' in Proposition 6.1.2: A Case for n=2
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MHB Complex Analysis: Does $\int_{C(0,10)} f(z)$ Equal 0?
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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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A Hausdorff property of projective space
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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 Describing homeomorphisms with the π1 function
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DMD is better without Ergodic Theory and Koopman Operators
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I Simpler Brunnian "rubberband" loops?
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MHB A function given by a logical expression write in the truth table.
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I Writing down an explicit homotopy
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I "Approximating Basis" -- Is there a contemporary term?
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I Broadly spiralling shape from partial sums of Zeta (0.5 + i t)
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I Showing that a group acts freely and discretely on real plane
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B Is the Quotient Topology of Real Numbers Homeomorphic to Real Numbers?
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I Is this generalization equivalent to usual Aposyndetic
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A Limits and Supremum: Is It True?
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MHB Is the convergence uniformly?
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B Open sets in quotient topology
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I Doing proofs with the variety function and the Zariski topology
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I A problem of completeness of a metric space
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I Proving a function f is continuous given A U B = X
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I Help with expression ##F(it)-F(-it)## in the Abel-Plana form
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CW complex for infinite holed torus? (Surface of infinite genus)
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I Solving Zeno's Paradox: The Flaw in the Notion of Infinity
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I Show R^2 \{(0,0)} and {(x,y) | 1 < sqrt(x^2+y^2) < 3} are homeomorphic
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MHB Determine the area, calculate the basis vectors and determine the inner product
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I An open set can be a closed interval?
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MHB Extrema and convergence of sequence
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MHB Calculate the volume of the set M
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MHB What % is 60M of 6 Billion
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MHB Help Me: Get the Support You Need
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MHB Limit Comparision Test: Get Help Now
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Topological Data Analysis - Persistent Homology
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MHB Harmonic function problem
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MHB Cauchy-Riemann Equations test problem
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MHB Understanding the Harmonic Function Problem
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I Continuity of an inverse of a function
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MHB Struggling with Complex Number Function? Need Help?
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MHB Complex number equation graph problem
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MHB Global Extrema of a Trigonometric Function
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MHB Lebesgue Outer Measure .... Carothers, Proposition 16.1 ....
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B What is the nature of dimensionality in 11 dimension M-theory?
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I Pseudometric Spaces: What Are They and Why Are They Important in Mathematics?
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A Something on Baire categories
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MHB Finding the Unique Solution of a Polar System with Variable Radius?
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I Negative curvature in low dimensions
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I Is there a "Nice" proof that R^2 is not disconnected when we remove 2 points
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A Topological Definition of Holes
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MHB Proving Topology in X: A Look at Union & Intersection
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I Munkres Chapter 5: Problem involving the Tychonoff Theorem
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A Curvilinear Coordinate System
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MHB Prove that series converges uniformly
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MHB Prove that the algebra generated is dense
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MHB Correctness of Statements about Set A in Metric Space X
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A Fourier transform of hyperbolic tangent
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MHB F doesn't have in (0,0) a local minimum
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MHB Points of the surface with minimum distance to the point (3,0,0)
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MHB How to show that T_k is the only polynomial of degree k with the specific properties?
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MHB F convex iff Hessian matrix positive semidefinite
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MHB Exploring Level Lines and Gradient in Multivariable Calculus
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MHB Is f differentiable in (0,0) ?
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MHB Can the Sum of Two Squares Ever Equal 3 Times a Perfect Square?
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MHB Piecewise function: differentiable but not continuously differentiable
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MHB F is partially differentiable in (0,0) but not total differentiable
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MHB Finding the Infimum and Supremum
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I ##(a_n) ## has +10,-10 as partial limits. Then 0 is also a partial limit
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A Exploring the Boundary of the 3-Sphere: A Topological Analysis
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MHB Uniform convergence - Length of graph
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MHB Convergence as for the cofinite topology on R
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I Proof check for Plancherel's theorem (Fourier Transform version)
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I Is [0,1] under the subspace topology Hausdorff, Compact, or Connected?
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The correct domain of self-adjointness for the Laplacian
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A What Topological Vector Spaces have an uncountable Schauder basis?
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MHB Understanding Example from Topics in Banach Space Integration
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I Jordan Measurement: Accuracy You Can Trust
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A Can falling factorials be a Schauder basis for formal power series?
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MHB Laplace Convolution: f(t)=-5t^2+9
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I Analytic continuation of Dilogarithm
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B Does uniform continuity of |f| imply uniform continuity of f?
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MHB How can we prove the convergence of recursive defined sequences?
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MHB Show that there is a 1-km section that he covers in 1.5 minutes
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MHB When is the Angle Maximum?
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MHB Proving Differentiability of f at $x_0$
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MHB Draw Angles & Find Values in Unit Circle
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I Problems with understanding the role of the partition of unity
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MHB Calculating derivatives for various functions
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MHB Value of f(1/2) using estimation for the remainder
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A Questions about Dynkin diagrams
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MHB Check convergence of integrals
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MHB Understanding Browder Proposition 3.14: Increasing Function & Discontinuities
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MHB Well-defined function that doesn't satisfy IVT
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MHB Proving Boundedness of Seq. $(a_n)$ Given Bound Seq. $(\frac{a_{n+1}}{a_n})$
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MHB Calculating Distance for Woman & Dog Walking Home
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MHB Composition of Two Continuous Functions .... Browder, Proposition 3.12 .... ....
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I A claim regarding Fourier Series
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I Riemann Integration ... Existence Result .... Browder, Theorem 5.12 ....
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MHB Riemann Integration ... Existence Result .... Browder, Theorem 5.12 ....
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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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