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 1-Forms .... Interpretation by Bachman ....
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MHB Understanding Lusin's Theorem for $\mathbb{R}$ and Its Proof
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MHB Directional Derivative Example .... SHifrin, Ch.3, Section 1, Example 3 ....
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MHB Power Series .... Abbott, Theorem 6.5.1 .... ....
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MHB Pointwise Convergence .... Abbott, Example 6.2.2 (iii) .... ....
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I Metric Homeomorphism: Isometry Equivalence?
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I Can we have a pasting lemma for uniform continuous functions
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I Hausdorff Metric: Definition 1 vs. Definition 2
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MHB Measure Theory - Existence of Fsigma set contained in measurable set
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MHB Are Injective R-Linear Mappings in C Necessarily Surjective?
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MHB Law of Cosines for C .... Remmert Section 1.3, Ch. 0 ....
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MHB How does Remmert derive the Cauchy-Schwarz Inequality in complex functions?
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I Flipping the sign in the definition of derivative
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I Result regarding signs and a limit
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I R-Linear and C-Linear Mappings.... Another Question ....
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MHB R-Linear and C-Linear Mapings .... ....
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B Spivak's Calculus as a Prerequisite for General Topology
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I Complex & Real Differentiability ... Remmert, Section 2, Ch 1
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A Diff. forms: M_a = {u /\ a=0 | u in L}
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MHB Complex and Real Differentiability .... Remmert, Section 2, Ch. 1 .... ....
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A Is There a Unique Hodge Star Operator for Any p-Vector in Differential Forms?
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MHB Is e^x a transcendental function?
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I The Chain Rule for Multivariable Vector-Valued Functions ....
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MHB The Chain Rule for Multivariable Vector-Valued Functions .... ....
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MHB Remark on the Definition of Differentials .... Lafontaine page 5 ....
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I Metric Spaces and Topology in Analysis
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MHB Multi-value Function: What & Why
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A Show that set is an orthonormal set in PC(0,l)
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MHB Differentiability of Multivariable Vector-Valued Functions .... ....
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MHB Relationship Between Total Derivatives and Directional Derivatives .... ....
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MHB Directional Derivatives .... Apostol, Section 12.2, Example 4 ....
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I How to prove that compact regions in surfaces are closed?
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MHB Properties of Functions of Bounded Variation
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MHB Bounded Variation - Difference of Functions
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MHB Proof of Apostol's Definition 3.2 and Theorem 3.3: Help Appreciated
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MHB Using Rolle's theorem to prove for roots (part 2)
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I Confused by the behavior of sqrt(z^2+1)
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MHB Using Rolle's theorem to prove for roots
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MHB Continuous and differentiability
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MHB Is the limit of the sequence $\left(1+\frac{1}{\sqrt{n}}\right)^n$ infinite?
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MHB Convergence and existence of constants
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MHB Are my ideas as for the convergence right?
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MHB Does the sequence $(a^n b^{n^2})$ converge for all values of $a$ and $b$?
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MHB Doesn't it suffice to pick the limit of the sequence?
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I Showing that a_n > 0 given its decreasing and lim a_n=0
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I Ordinals .... Searcoid, Corollary 1.4.5 .... ....
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I Ordinals .... Searcoid, Theorem 1.4.6 .
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I Showing that an infinite sum converges when a sign in the denominator is flipped
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I Limsup(a+b) = limsup(a) + limsup(b)
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I Principal branch of the log function
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I Proper Subsets of Ordinals .... .... Searcoid, Theorem 1.4.4 .
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I Proper Subsets of Ordinals .... .... Another Question .... ....
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MHB Finding Supremum and Infimum of Sets with Inequalities
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I How Do We Prove a Subset of an Ordinal is Well-Ordered?
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I Series of even and odd subsequences converge
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MHB What is the Property of Infimum for Sets?
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MHB Are these two propositions equivalent when dealing with subsets of real numbers?
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MHB Problems for Cauchy Integral Formula
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I Learning the theory of the n-dimensional Riemann integral
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MHB Is Φ a Bijective Map from Power Set to Characteristic Functions?
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I How Is Divergence to Infinity Defined in Contrast to General Divergence?
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I Projecting Möbius Strip Edge: Learn How in 2D Plane
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MHB Proving that solutions of a equation are irrational
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MHB How can we compare the lower envelope of a function with the function itself?
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MHB Lower SemiContinuity Problem: Proofs & Step Funcs
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MHB How Can We Approximate a Continuous Function with a Piece-Wise Linear Function?
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A How to prove that cuboids are Lebesgue measurable?
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MHB Every Closed Set in R has a Countable Dense Subset
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MHB Plus or minus question for the complex log
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MHB Can I Find Examples for Continuous Improvement?
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MHB Find Limit of cos(x) with Inequalities | Part (b) Help
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I Distribute Limit over Addition: Evaluating w/o Knowing Convergence
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MHB Understanding the Cauchy-Schwarz Inequality
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MHB Is Showing One ε Enough to Prove Discontinuity?
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MHB Can Dividing by Sin x Help Prove Continuity at x = 0?
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A What uniquely characterizes the germ of a smooth function?
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I Equivalence of Covering Maps and Quotient Maps
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I Intuition - Cauchy integral theorem
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MHB Real Analysis, Sequences in relation to Geometric Series and their sums
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MHB Set of points on the complex plane
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MHB Proving Modulus Inequality for Complex Numbers
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MHB Real Analysis, liminf/limsup inequality
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MHB Does the Norm of a Linear Integral Operator Equal Its Spectral Radius?
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I How Does the Bernstein-Schröder Theorem Establish Set Equivalence?
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A Higher Order Derivative Test and Germs
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I Proof Explanation: Showing an extension to a continuous function
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I Understanding the "branch cut argument"
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I Topology vs Differential Geometry
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I Munkres-Analysis on Manifolds: Theorem 20.1
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I Coordinate functions of a many-to-1 function
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Insights Hilbert Spaces and Their Relatives - Definitions
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I Uniqueness of tangent space at a point
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MHB Proving Injectivity of a Vector-Valued Function Using the Mean Value Theorem
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MHB F has an uniquely defined global minimum
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MHB Image of each open subset is open
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A Is There a Boundary Point Where the Holomorphic Function Equals Zero?
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B Geometrical Test for Immersion of Klein Bottle in Higher Dimensional Manifold
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B Infinite dimensional Hilbert Space
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A Why Must the Constant in Hilbert Space Function B[f(x)] Be Defined as Shown?
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I What is the usefulness of topology in understanding functions?
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