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.
B How Do Dedekind Cuts Affect Addition and Negative Numbers?
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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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I Circuits or edge-disjoint unions of circuits in a connected graph
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I Can you somehow make left handed helix into a right handed?
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MHB Outer measure .... Axler, Result 2.8 ....
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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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B Aperiodic Tiling with a single tile shape
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A Regarding fibrations between smooth manifolds
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I Geometry of series terms of the Riemann Zeta Function
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I I need a mapping from the unit Hypercube [0,1]^n to a given simplex
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I Discrete Subrings of Complex Numbers: Topology of Rings
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MHB Checking Proof of Theorem 6.2.8 Part (ii)
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I I would like opinions of the latest draft of my note - Integration
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I Upper and Lower Darboux Sum Inequality
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I Original definition of Riemann Integral and Darboux Sums
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MHB How to Prove \(\text{vol}_n (B) = \text{vol}_n (B') + \text{vol}_n (B'')\)?
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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 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 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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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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MHB Can This Forgotten Formula Simplify the Laplace Transform of \(y(t)^3\)?
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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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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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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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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 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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