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.
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 the Role of the Identity Map in Fundamental Group Theory
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MHB How to Prove a Complex Number Equation and Its Trajectory Forms a Circle?
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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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MHB Can This Forgotten Formula Simplify the Laplace Transform of \(y(t)^3\)?
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Is the Integral Inequality Possible to Prove for Certain Parameters?
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A Ref: "Standard" Action of S^1 on S^n ?
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B Is the Texan Conjecture a mathematical truth or a myth?
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MHB The Supremum of a Set is not an Interior Point
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I If a sequence converges, then all subsequences of it have same limit
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MHB How Can I Tackle Difficult Questions Effectively?
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A Laurent series for algebraic functions
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MHB Proving Measure Space Properties of $(X,\bar{\mathcal{B}} ,\bar{\mu})$
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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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I How can I use the concept of a proper map to show that a set is bounded?
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I ##\epsilon - \delta## proof and algebraic proof of limits
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MHB Prove that the function is monotonic and not decreasing
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B Is the 10 Dimensional Poincaré Group a Coincidence?
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A What does the metric of a 6D space with 3 compactified dimensions look like?
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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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MHB Proving Relatively Compactness in C([a, b]) using Arzelá-Ascoli Theorem
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MHB Prove that it converges uniformly
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I Functions.wolfram.com accepted and published my formula for Gamma Fn
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I Proving a convergent sequence is bounded
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I How Does Fourier Transform Analyze Beats in Signals?
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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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MHB Discover the Limit of a Sequence with Easy-to-Follow Steps
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A Confused by a theorem in Milnor-Stasheff
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MHB How Do Riemann Integrals Handle Function Splits and Summations?
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I Looking for Someone Strong in Analysis
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MHB Recursive Function for Virus Spread: Finding the General Solution
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I Hopf Fibration, torus with fibers, do it 2 ways?
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MHB Proving Lemma 3.3 of L&S: Further Aspects of the Proof
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I What's the definition of "periodic extension of a function"?
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MHB An Aspect of Lemma 3.3 .... Laczkovich and Vera T Sos .... L&S ....
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I Show that (0, ∞) is homeomorphic to (0, 1)
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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 How can we prove the inequality for the supremum and infimum of f*g and f*g?
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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 Does This Sequence Converge Uniformly?
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B Why Is the Trick for Open Sets in Quotient Topology Valid?
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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 Percentage Am I Asking For If I Want 60 Million Out of 60 Billion Profit?
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MHB Need Support? Discover How to Get Help!
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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 How to Solve a Harmonic Function Problem Involving Partial Derivatives?
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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 Is the Assertion Derived from a General Theorem Trivial or Interesting?
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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 What Are n-Dimensional Holes in Topology?
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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 How Do You Determine the Mapping Functions in 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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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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