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 Are the Metrics \(d_1\), \(d_2\), and \(d_{\infty}\) Strongly Equivalent?
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MHB Is the relation between limit points and closed sets clear? (Wondering)
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Undergrad How Does Vector Subtraction Relate to Topology?
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MHB Proof that Arcsin x is continuous ....
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MHB Differentiating Complex Square Root Function: Bruce P. Palka, Ex. 1.5, Ch. III
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MHB Complex Square Root Function: Qs from Bruce P. Palka's Ex. 1.5, Ch. III
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MHB Where Does the Sign of n Matter in Palka's Examples?
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MHB How is Equation (1) Equivalent to the Derivative Definition in Theorem 7.1?
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Graduate DFT Meaning of k's Greetings: Understanding Wavelength & Interval Length
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Undergrad How to derive the Fourier transform of a comb function
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Undergrad Help Solve Munkres Question: Limit Point Compact Subspace in Hausdorff Space
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Undergrad Complex Fourier transform (represented by Σ)
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Undergrad How do charts on differentiable manifolds have derivatives without a metric?
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Graduate Fourier transform and derivation
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Undergrad Differentiable manifolds over fields other than R, C
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MHB Verify Gamelin's Remark: Complex Square and Square Root Functions
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MHB Show that there is no order relation on K
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MHB Show that there exists a bijection
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MHB Prove f is One-to-One: (a) and (b) | Help with Choosing Inverse Formula
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Undergrad Discrete Topology and Closed Sets
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Undergrad What is wrong with this proof? (divergence of the harmonic series)
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MHB Complex Derivative .... Remark in Apostol, Section 16.1 .... ....
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MHB Proof of an Infimum Being Equal to the Negative Form of a Supremum ()
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Undergrad Trouble with infinity and complex numbers
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High School Understanding the Quadratic Form Identity in Two-Variable Equations
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MHB Understanding Differentiability and Continuity in Complex Analysis
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MHB Upper and Lower Linits (lim sup and lim inf) - Denlinger, Theorem2.9.6 (b) ....
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MHB Another Question on Upper and Lower Limits .... Denlinger, Theorem 2.9.6 (a)
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MHB Proof of Sohrab's Proposition 2.2.39 (a) | Upper & Lower Limits
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Undergrad Assigning a value for integrating a divergent oscillatory function to infinity
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MHB Upper and Lower Linits (lim sup and lim inf) - Sohrab Proposition 2.2.39 (b) ....
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MHB How Does Theorem 4.29 Illustrate Continuity Issues in Inverse Functions?
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Undergrad Different metrics in different dimensions
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MHB Functions Continuous on Comapct Sets .... Apostol, Theorem 4.25 ....
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MHB Limits of Complex Functions .... Zill & Shanahan, Theorem 3.1.1/ A1
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MHB The Metric Space R^n and Sequences .... Remark by Carothers, page 47 ....
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Graduate How Does the Chain Rule Apply to Pushforwards in Differential Geometry?
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MHB Carothers' Definitions: Neighborhoods, Open Sets, and Open Balls
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MHB Understand Example 3.10 (b) Karl R. Stromberg, Chapter 3: Limits & Continuity
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MHB Open Balls in a Normed Vector Space .... Carothers, Exercise 32
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Undergrad Division of a complex number by zero
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MHB Neighbourhoods and Open Neighbourhoods .... Browder, Proposition 6.8 .... ....
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MHB Baire Category Theorem .... Stromberg, Theorem 3.55 .... ....
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Graduate Baire Category Theorem .... Stromberg, Theorem 3.55 .... ....
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MHB Understanding Topology: Closure, Boundary & Open/Closed Sets
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Graduate Fourier Series = Re(Power Series)
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MHB Why is \( c'' \) an Upper Bound for \( U \cap [a, b] \) in Theorem 3.47?
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MHB Equivalent Statements to COmpactness .... Stromberg, Theorem 3.43 .... ....
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Graduate General formula for lenses without spherical abberation
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MHB Maximum Likelihood Estimation Formula Simplification and Solution for p?
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MHB Countably Dense Subsets in a Metric Space .... Stromberg, Lemma 3.44 .... ....
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MHB Heine-Borel Theorem in R^n .... Stromberg, Theorem 3.40 .... ....
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MHB Compact Topological Spaces .... Stromberg, Theorem 3.36 .... ....
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MHB Proving a limit to infinity using epsilon-delta
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MHB Compact Topological Spaces .... Stromberg, Example 3.34 (c) .... ....
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MHB Open Subsets in a Metric Space .... Stromberg, Theorem 3.6 ... ....
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MHB Finding Cluster Points/Accumulation Points
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MHB Why is the Series Absolutely Convergent for Sequences in l^2(N)?
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Undergrad Continuity and Open Sets .... Sohrab, Theorem 4.3.4 .... ....
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MHB Heine-Borel Theorem .... Sohrab, Theorem 4.1.10 .... ....
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MHB Closed and Bounded Intervals are Compact .... Sohrab, Propostion 4.1.9 .... ....
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Undergrad Compact Subsets of R .... Sohrab, Proposition 4.1.8 .... ....
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MHB Compact Subsets of R .... Sohrab, Proposition 4.1.8 .... ....
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Graduate Fractional Calculus and Residues
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MHB Compact Subsets of R .... Sohrab, Proposition 4.1.1 (Lindelof)
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Undergrad Compact Subsets of R .... Sohrab, Proposition 4.1.1 (Lindelof) ....
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Graduate Functional differentiability: Frechet, but not Hadamard?
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Graduate A question about the proof of the simple approximation lemma
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MHB Lindelof Covering Theorem .... Apostol, Theorem 3.28 ....
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Undergrad Lindelof Covering Theorem .... Apostol, Theorem 3.28 ....
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Graduate Mapping of algebraic function to Riemann surface?
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Graduate CW complex for infinite holed torus? (Surface of infinite genus)
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Graduate Topology: Munkres - Urysohn lemma
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Graduate Identifying Compact Sets in the Slitted and Moore Planes: What's the Method?
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Graduate Does SU(2) Commutativity Conflict with Its Non-Euclidean Structure?
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Graduate Is the Integral Inequality Possible to Prove for Certain Parameters?
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Graduate Inquiry: Wavelet factorisation / Daubechies method /
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Graduate Two definitions of locally compact
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Graduate How to Estimate the Operator Norm ||A||_2 for a Difference Operator?
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MHB The Number e .... Another Issue/Problem Regarding Sohrab Proposition 2.3.15 ....
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MHB The Number e .... Another Question Regarding Sohrab Proposition 2.3.15 ....
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MHB Proposition 2.3.15: Understanding Sohrab's Basic Real Analysis Proof
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Undergrad The Number e .... Sohrab Proposition 2.3.15 ....
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Graduate Proof of the L'Hôpital Rule for the Indeterminate Form
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MHB First Comparison Test for Series .... Sohrab Theorem 2.3.9 ....
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Graduate Is it related to measure theory - Help
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Graduate The correct domain of self-adjointness for the Laplacian
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Graduate How to generalize Newtonian and Lagrangian mechanics
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MHB Infinite Series .... Sohrab Exercise 2.3.10 (1) .... ....
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Graduate Residue Proof of Fourier's Theorem Dirichlet Conditions
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Graduate Question about bounded functions
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MHB Absolute and Conditional Convergence .... Sohrab Proposition 2.3.22 ....
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Graduate Can the Fejér Kernel Be Approximated by Polynomials?
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Undergrad Necessity of absolute value in Cauchy Schwarz inequality
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MHB P-series .... Sohrab, Proposition 2.3.12 .... ....
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Graduate How are topological spaces applied in the realm of physics?
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MHB The Number e .... Sohrab Proposition 2.3.15 ....
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MHB Convergence of Geometric Series .... Sohrab, Proposition 2.3.8 .... ....
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Undergrad Application of Supremum Property .... Garling, Remarks on Theorem 3.1.1
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Undergrad Real Numbers & Sequences of Rationals .... Garling, Corollary 3.2.7 ....
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