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 Complex number equation graph problem
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MHB Local & global extrema
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B What is the nature of dimensionality in 11 dimension M-theory?
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MHB Prove that the function is monotonic and not decreasing
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B 10 dimensional Poincaré group
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I Riemannian pseudometric space
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A Something on Baire categories
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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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MHB Prove that series converges uniformly
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MHB Arzela-Acoli Theorem
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MHB Prove that the algebra generated is dense
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MHB Prove that it converges uniformly
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MHB Statements about set A
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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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575
MHB Points of the surface with minimum distance to the point (3,0,0)
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622
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 Level lines and gradient
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MHB Is f differentiable in (0,0) ?
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MHB How to show this result?
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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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567
MHB Find Limit of Sequence - Get Help Now!
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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 The 3-sphere has no boundary
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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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MHB Riemann Integral-Questions
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I Proof check for Plancherel's theorem (Fourier Transform version)
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I Subspace Topology Basics
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A What Topological Vector Spaces have an uncountable Schauder basis?
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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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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 Convergence of sequence
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MHB Complex Analysis: Does $\int_{C(0,10)} f(z)$ Equal 0?
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688
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 Differentiability of f
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MHB Angles in unit circle
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I Problems with understanding the role of the partition of unity
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MHB Calculate derivatives
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MHB Value of f(1/2) using estimation for the remainder
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MHB Check convergence of integrals
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MHB Well-defined function that doesn't satisfy IVT
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MHB Calculating Distance for Woman & Dog Walking Home
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MHB Ratio test - Root test
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A Compute Lebesgue integral as (improper) Riemann integral
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I Curve of zeta(0.5 + i t) : "Dense" on complex plane?
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B Question on a property of a function which is not a metric
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I Basic question on tensor analysis
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26
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MHB A function given by a logical expression write in the truth table.
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I Any Good Lecture Series on Complex Analysis?
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B Applications of topological spaces not homeomorphic to R^n in physics
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I Questions on metric spaces
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A Integrability along a Hilbert space?
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I Is U(1) the same as SU(1)?
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A Is this Fourier transformation an eigenproblem?
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I Help Finding the Correct Approach to this Proof (Intro Real Analysis)
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I Frechet Derivatives & Optimization - Mechanics Example
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A Frechet of a linear operator
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I About groups and continuous curves
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I About Homology
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MHB Determine the area, calculate the basis vectors and determine the inner product
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I Why is [0,1] compact in the case of a collection of open neighborhoods?
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MHB Solving a complex value equation
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A Topological Basis in l2 Space: Why?
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MHB What % is 60M of 6 Billion
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MHB Sequence of functions : pointwise & uniform convergence
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MHB Convergence of series
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MHB Using Cauchy Integral Formula for Laurent Series Coefficients
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I Differential analysis: convex functions
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I Gamma function/partial fractions (a problem from my Insights article)
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I The Set of Borel Sets .... Axler Pages 28-29 .... ....
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MHB The Set of Borel Sets .... Axler Pages 28-29 .... ....
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I Continuity of an inverse of a function
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MHB Smallest Sigma Algebra .... Axler, Example 2.28 ....
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I Smallest Sigma Algebra .... Axler, Example 2.28 ....
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I Courant and Fritz, Construction of the real numbers
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I Inequality from a continuity exercise
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I Sigma Algebras .... Axler, Page 26 ....
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MHB Sigma Algebras .... Axler Page 26 ....
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A The map from a complex torus to the projective algebraic curve
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I Translation Invariance of Outer Measure .... Axler, Result 2.7 ....
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MHB Translation Invariance of Outer Measure .... Axler, Result 2.7 ....
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I Lebesgue Outer Measure .... Carothers, Proposition 16.2 (i) ....
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MHB Outer measure of an open interval ....
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I Lebesgue Outer Measure .... Carothers, Proposition 16.1 ....
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MHB Lebesgue Outer Measure .... Carothers, Proposition 16.2 (i) ....
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MHB Lebesgue Outer Measure .... Carothers, Proposition 16.1 ....
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MHB Outer measure of a closed interval .... Axler, Result 2.14 ....
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MHB Outer measure .... Axler, Result 2.14 .... Another Question ....
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3
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MHB Lebesgue Outer Measure .... Carothers, Proposition 16.1 ....
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Topology and Analysis

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Participate in expert discussion on topology and analysis topics. It's the study of geometric properties and spatial relations unaffected by the continuous change of shape or size of figures.

This includes point-set topology, Real, complex, harmonic and functional analysis. Also the topics of measure and integration theory apply.

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