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 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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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 Why is \( T_k \) the Unique Polynomial of Degree \( k \) with These Properties?
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MHB F convex iff Hessian matrix positive semidefinite
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MHB What Are Level Lines and Gradients in Multivariable Calculus?
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MHB Is f Differentiable at (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 Is There a Simple Method to Analyze the Boundary of the 3-Sphere?
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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 Is [0,1] under the subspace topology Hausdorff, Compact, or Connected?
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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 Maximum Angle for Viewing a Tower from an Airplane?
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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 Do Dynkin Diagrams Only Describe Lie Algebras?
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MHB Do These Integrals Converge or Diverge?
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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 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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A Compute Lebesgue integral as (improper) Riemann integral
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MHB The Riemann and Darboux Integrals .... Browder, Theorem 5.10 .... ....
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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 Can Tensors of Any Rank Be Approximated by Matrices?
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MHB Differentials and Jacobians .... Remarks After Browder Prposition 8.21 ....
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I Any Good Lecture Series on Complex Analysis?
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MHB The Chain Rule in n Dimensions .... Browder Theorem 8.15 - Another Question ....
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MHB Operator Norm and Cauchy Sequence .... Browder, Proposition 8.7 ....
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MHB Calculations with stepfunction(heaviside)
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B Applications of topological spaces not homeomorphic to R^n in physics
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I How Do Metric Space Properties Relate to Continuity?
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A Integrability along a Hilbert space?
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I Can a U(1) Generator be Normalized to SU(1) through Determinant Condition?
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MHB Understanding Theorem 3.4: Mean Value Theorem & Cauchy Riemann Equations
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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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MHB Complex Function Theory: Explaining Example 1.5, Section 1.2, Chapter III
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A Is the Frechet Derivative of a Bounded Linear Operator Always the Same Operator?
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I About groups and continuous curves
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I What are the applications of homology in understanding spaces and shapes?
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MHB Question for Intermediate Analysis ()
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MHB Infinite dimentional subspace need not be closed
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I Why is [0,1] compact in the case of a collection of open neighborhoods?
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MHB Proof of the Equality of Supremums (Or Something Like That Anyway :) )
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MHB Infimum and Supremum of a Set (Need Help Finding Them)
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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 Sequence of functions : pointwise & uniform convergence
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MHB Checking Convergence of Series: Inequalities & Tests
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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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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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