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.
Undergrad Trying to understand why a set is both open and closed
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MHB Find the square roots of 4*sqrt(3)+4(i)
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Undergrad Existence of Directional Derivative in Normed Linear Space
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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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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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MHB Solving Complex Number With Negative Fractional Exponent: i^(-21/2)
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Graduate Analytical function from numerable point set
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MHB Ap1.3.51 are complex numbers, show that
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Undergrad Metric Homeomorphism: Isometry Equivalence?
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Undergrad Can we have a pasting lemma for uniform continuous functions
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Undergrad 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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Undergrad Flipping the sign in the definition of derivative
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Undergrad Result regarding signs and a limit
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Undergrad R-Linear and C-Linear Mappings.... Another Question ....
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MHB R-Linear and C-Linear Mapings .... ....
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High School Spivak's Calculus as a Prerequisite for General Topology
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Undergrad Complex & Real Differentiability ... Remmert, Section 2, Ch 1
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Graduate 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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MHB Why is ln(k) a Complex Number When k is a Positive Integer?
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Graduate 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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Undergrad 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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Undergrad Metric Spaces and Topology in Analysis
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MHB Multi-value Function: What & Why
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Graduate 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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Undergrad 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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Undergrad 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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Undergrad Showing that a_n > 0 given its decreasing and lim a_n=0
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Undergrad Ordinals .... Searcoid, Corollary 1.4.5 .... ....
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Undergrad Ordinals .... Searcoid, Theorem 1.4.6 .
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Undergrad Showing that an infinite sum converges when a sign in the denominator is flipped
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Undergrad Limsup(a+b) = limsup(a) + limsup(b)
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Undergrad Principal branch of the log function
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Undergrad Proper Subsets of Ordinals .... .... Searcoid, Theorem 1.4.4 .
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Undergrad Proper Subsets of Ordinals .... .... Another Question .... ....
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MHB Finding Supremum and Infimum of Sets with Inequalities
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Undergrad How Do We Prove a Subset of an Ordinal is Well-Ordered?
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Undergrad 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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Undergrad 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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Undergrad How Is Divergence to Infinity Defined in Contrast to General Divergence?
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Undergrad Projecting Möbius Strip Edge: Learn How in 2D Plane
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Undergrad Complex exponential to a power
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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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Graduate 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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Undergrad Ambiguities of the "...." notation
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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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Undergrad Complex analysis - removable singular points
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