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 Absolute and Conditional Convergence .... Sohrab Proposition 2.3.22 ....
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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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MHB What Are the Key Insights from D. J. H. Garling's Theorem 3.1.1?
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MHB Understanding Garling's Corollary 3.2.7 on Real Numbers and Rational Sequences
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High School Precision Representation of Vectors Using a Spiral on a Sphere
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MHB Partial Order .... Garling, pages 9-10, Volume I ,,,
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MHB Open and Closed Sets in R^n .... Duistermaat and Kolk, Lemma 1.2.11 ....
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MHB Uniform norm .... Garling Section 11.2 Normed Saces .... also Example 11.5.7
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Graduate Reproducing Kernel Hilbert Spaces
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MHB Norm bounded Sets .... remarks by Garling in Section 11.2 Normed Spaces ....
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MHB Open Sets in R^n .... Duistermaat and Kolk, Lemma 1.2.5 ....
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MHB Bounded in Norm .... Garling, Section 11.2: Normed Spaces ....
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MHB Necessary and Sufficient Meaning of Isometries by D. J. H. Garling
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Undergrad Lemma 1.2.3 - Ethan.D.Bloch - The Real Numbers and Real Analysis
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Graduate What are the equality conditions for proving strict convexity?
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MHB Gram-Schmidt Orthonormalization .... Garling, Corollary 11.4.2 ....
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MHB Gram_Schmidt Orthonormalization .... Remarks by Garling, Section 11.4 .... ....
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MHB How Do We Know the Annihilator Operation Is Associative?
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MHB Prop 11.3.5-4: Peter's Help with Garling's The Annihilator of a Set
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MHB Open and Closed Sets .... Conway, Example 5.3.4 (b) .... ....
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MHB Proof of the Cauchy-Schwarz Iequality .... Garling, Proposition 11.3.1 .... ....
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MHB Pseudometrics .... Garling, Proposition 11.1.13 .... ....
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Undergrad Bounded in Norm .... Garling, Section 11.2: Normed Spaces ....
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Undergrad Metric Spaces .... the Uniform Metric .... Garling, Proposition 11.1.11
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MHB Metric Spaces .... the Uniform Metric .... Garling, Proposition 11.1.11 ....
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Undergrad Why do these functions form complete orthogonal systems in the Hilbert space?
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MHB Radius and Interval of Convergence for (x/sin(n))^n
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Undergrad Can someone explain these two examples of an open set
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Undergrad Why Restrict Derivatives to Intervals?
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Undergrad Parametrized Set .... McInerney, Example 3.3.3 .... ....
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MHB Integral Over Unit Sphere of Inner Product
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Undergrad Tangent Spaces and Subspaces .... McInerney Theorem 3.3.13 ....
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Graduate Mechanical steps for the natural-neighbor interpolation
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Undergrad Pole Identification Using Block Diagram Reduction
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MHB Finding Lebesgue Decomposition for a Measure Defined by an Integral
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Undergrad On the topological proof of the Fundamental Theorem of Algebra
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Graduate Why does the characteristic function not converge in the L1 space?
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MHB McInerney Example 3.1.5: Multivariable Differentiation Q&A
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Undergrad Finding all valid surfaces that go through a vector field
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MHB Multivariable Differentiation .... McInerney Definition 3.1.1
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Graduate What do the notations in functional analysis mean for a given function?
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Undergrad Differential Forms.... Another question.... Browder, Sec 13.1
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Undergrad Differential Forms & Tensor Fiekds .... Browder, Section 13.1
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Undergrad Wedge Product and Determinants .... Tu, Proposition 3.27 ....
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Undergrad Permutations and Determinants .... Walschap, Theorem 1.3.1 ...
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Undergrad Anticommutativity of Wedge Product .... Tu, Proposition 3.21
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Undergrad The Wedge Product .... Tu, Section 3.7
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Undergrad Tensors & the Alternation Operator .... Browder, Propn 12.25
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Undergrad Space of Alternating Tensors of Rank r.... (Browder, 12.22)
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Undergrad Which branch of mathematics talks about this?
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Graduate Where is the actual space inside a tesseract?
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High School Finite distance between two points
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MHB Vitali Covering: Proving Finite Interval Covering for m*(E)<∞
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MHB "Approximation to the Identity" and "Convolution" Proof
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MHB The Dual Space and Covectors .... Browdwer, Theorem 12.2 and Corollaries ....
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MHB Dual Space .... Loring Tu, Section 3.1, page 19 .... ....
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MHB The Dual Space and Differential Forms .... ....
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MHB Rank One Tensors .... Fortney Appendix A, Section A2 ....
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MHB The Space of 2-Forms .... Fortney, Darling and Weintraub ....
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Undergrad Understanding why ##(y_n)_n## is a bounded sequence
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Undergrad Showing that a function is analytic
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MHB Remarks by Fortney Following Theorems on Directional Derivative ....
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MHB Approx. in $L^p$: Proving Existence of Subseq & $g$
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MHB Proving Density of $S$ in $L^{p'}(E)$ for $g \in L^p(E)$
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Undergrad Error estimate for iterative convergence
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MHB Piecewise Continuous and piecewise smooth functions
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Undergrad How to think of S1 (circle) abstractly
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MHB Real Analysis - Convergence to Essential Supremum
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Undergrad How to confirm the function has genus 116?
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Undergrad Completeness of a basis function
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Undergrad Do partial derivatives commute in general?
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Graduate Structure preserved by strong equivalence of metrics?
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Graduate Same open sets + same bounded sets => same Cauchy sequences?
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MHB The Derivative in Several Variables .... Hubbard and Hubbard, Section 1.7 ....
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MHB Finding border points and then interior points
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Undergrad Trying to understand why a set is both open and closed
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MHB Convex Functions: Find $f,g$ Satisfying f(x)=g(x) iff x is an Integer
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Undergrad Topology Words: Reasons for the particular names
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MHB Proving Convexity of $f: \mathbb{R} \to \mathbb{R}$
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MHB Orthogonal vector projection and Components in Orthogonal Directions ....
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Undergrad Open balls contained in other open balls
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Undergrad Understanding the definition of continuous functions
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Undergrad Using the Baire Category theorem
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MHB Does the Series Sum of Differences Converge Given a Contractive Condition?
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MHB Proving Convergence of a Sequence with a Geometric Condition
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MHB Finding the Limit Inferior and Limit Superior of a Sequence
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MHB Show existence of subsequences
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MHB Sequence has convergent subsequence
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MHB The Space of All Derivations at a point p .... Tu, Theorem 2.2 .... ....
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MHB Tangent Vectors in R^n as Derivations ....
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MHB Why Can't Two Functions Cover the Unit Circle?
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MHB Lusin's Theorem - Infinite Measure and not Real-Valued Extensions
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MHB Taylor's Theorem .... Loring W. Tu, Lemma 1.4 .... ....
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MHB Geometric Interpretation of k-Forms from H&H's Vector Calculus
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MHB Metric spaces and normed spaces
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