Topology and Analysis Forum

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.

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Operator norm --- Remarks by Browder After Lemma 8.4 ....

  • Math Amateur
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Operator Norm for Linear Transformations: Browder Ch. 8, Section 8.1, Page 179

  • Math Amateur
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Operator Norm .... differences between Browder and Field ....

  • Math Amateur
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Undergrad Embedding homeomorphic manifolds

  • Q-1
  • · Replies 42 ·
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The metrices are topologically but not strongly equivalent

  • mathmari
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The Elusive Field Structure of $\mathbb{R}^n$ Beyond $n=2$

  • Math Amateur
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How do I solve for a_3 in a complex Fourier series?

  • Tan Thom
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Is the relation between limit points and closed sets clear? (Wondering)

  • mathmari
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Undergrad How Does Vector Subtraction Relate to Topology?

  • doggydan42
  • · Replies 19 ·
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Proof that Arcsin x is continuous ....

  • Math Amateur
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Complex Square Root Function: Qs from Bruce P. Palka's Ex. 1.5, Ch. III

  • Math Amateur
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Where Does the Sign of n Matter in Palka's Examples?

  • Math Amateur
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How is Equation (1) Equivalent to the Derivative Definition in Theorem 7.1?

  • Math Amateur
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Graduate DFT Meaning of k's Greetings: Understanding Wavelength & Interval Length

  • SchroedingersLion
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Undergrad How to derive the Fourier transform of a comb function

  • arcTomato
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Undergrad Help Solve Munkres Question: Limit Point Compact Subspace in Hausdorff Space

  • facenian
  • · Replies 8 ·
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Undergrad Complex Fourier transform (represented by Σ)

  • arcTomato
  • · Replies 4 ·
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Undergrad How do charts on differentiable manifolds have derivatives without a metric?

  • jackferry
  • · Replies 20 ·
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20

Graduate Fourier transform and derivation

  • arcTomato
  • · Replies 7 ·
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Undergrad Differentiable manifolds over fields other than R, C

  • WWGD
  • · Replies 13 ·
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Verify Gamelin's Remark: Complex Square and Square Root Functions

  • Math Amateur
  • · Replies 3 ·
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Show that there is no order relation on K

  • mathmari
  • · Replies 9 ·
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Show that there exists a bijection

  • mathmari
  • · Replies 8 ·
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8

Prove f is One-to-One: (a) and (b) | Help with Choosing Inverse Formula

  • AutGuy98
  • · Replies 2 ·
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Undergrad Discrete Topology and Closed Sets

  • joshthekid
  • · Replies 12 ·
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12

Undergrad What is wrong with this proof? (divergence of the harmonic series)

  • BWV
  • · Replies 6 ·
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Complex Derivative .... Remark in Apostol, Section 16.1 .... ....

  • Math Amateur
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Proof of an Infimum Being Equal to the Negative Form of a Supremum ()

  • AutGuy98
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Undergrad Trouble with infinity and complex numbers

  • Troxx
  • · Replies 12 ·
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12

High School Understanding the Quadratic Form Identity in Two-Variable Equations

  • Heidi
  • · Replies 6 ·
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Understanding Differentiability and Continuity in Complex Analysis

  • Math Amateur
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Upper and Lower Linits (lim sup and lim inf) - Denlinger, Theorem2.9.6 (b) ....

  • Math Amateur
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Another Question on Upper and Lower Limits .... Denlinger, Theorem 2.9.6 (a)

  • Math Amateur
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Proof of Sohrab's Proposition 2.2.39 (a) | Upper & Lower Limits

  • Math Amateur
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6

Undergrad Assigning a value for integrating a divergent oscillatory function to infinity

  • Swamp Thing
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How Does Theorem 4.29 Illustrate Continuity Issues in Inverse Functions?

  • Math Amateur
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Undergrad Different metrics in different dimensions

  • Bob3141592
  • · Replies 2 ·
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Functions Continuous on Comapct Sets .... Apostol, Theorem 4.25 ....

  • Math Amateur
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Limits of Complex Functions .... Zill & Shanahan, Theorem 3.1.1/ A1

  • Math Amateur
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The Metric Space R^n and Sequences .... Remark by Carothers, page 47 ....

  • Math Amateur
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Graduate How Does the Chain Rule Apply to Pushforwards in Differential Geometry?

  • sanad
  • · Replies 7 ·
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Carothers' Definitions: Neighborhoods, Open Sets, and Open Balls

  • Math Amateur
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Understand Example 3.10 (b) Karl R. Stromberg, Chapter 3: Limits & Continuity

  • Math Amateur
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Open Balls in a Normed Vector Space .... Carothers, Exercise 32

  • Math Amateur
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Undergrad Division of a complex number by zero

  • dyn
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Neighbourhoods and Open Neighbourhoods .... Browder, Proposition 6.8 .... ....

  • Math Amateur
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Baire Category Theorem .... Stromberg, Theorem 3.55 .... ....

  • Math Amateur
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Graduate Baire Category Theorem .... Stromberg, Theorem 3.55 .... ....

  • Math Amateur
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Understanding Topology: Closure, Boundary & Open/Closed Sets

  • Math Amateur
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Graduate Fourier Series = Re(Power Series)

  • joeblow
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Why is \( c'' \) an Upper Bound for \( U \cap [a, b] \) in Theorem 3.47?

  • Math Amateur
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Equivalent Statements to COmpactness .... Stromberg, Theorem 3.43 .... ....

  • Math Amateur
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Graduate General formula for lenses without spherical abberation

  • mfb
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Heine-Borel Theorem in R^n .... Stromberg, Theorem 3.40 .... ....

  • Math Amateur
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Compact Topological Spaces .... Stromberg, Theorem 3.36 .... ....

  • Math Amateur
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Proving a limit to infinity using epsilon-delta

  • brooklysuse
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Compact Topological Spaces .... Stromberg, Example 3.34 (c) .... ....

  • Math Amateur
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Open Subsets in a Metric Space .... Stromberg, Theorem 3.6 ... ....

  • Math Amateur
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Finding Cluster Points/Accumulation Points

  • brooklysuse
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Why is the Series Absolutely Convergent for Sequences in l^2(N)?

  • Math Amateur
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Undergrad Continuity and Open Sets .... Sohrab, Theorem 4.3.4 .... ....

  • Math Amateur
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Heine-Borel Theorem .... Sohrab, Theorem 4.1.10 .... ....

  • Math Amateur
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Closed and Bounded Intervals are Compact .... Sohrab, Propostion 4.1.9 .... ....

  • Math Amateur
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Undergrad Compact Subsets of R .... Sohrab, Proposition 4.1.8 .... ....

  • Math Amateur
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Compact Subsets of R .... Sohrab, Proposition 4.1.8 .... ....

  • Math Amateur
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Graduate Fractional Calculus and Residues

  • Harrisonized
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Compact Subsets of R .... Sohrab, Proposition 4.1.1 (Lindelof)

  • Math Amateur
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Undergrad Compact Subsets of R .... Sohrab, Proposition 4.1.1 (Lindelof) ....

  • Math Amateur
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Graduate Functional differentiability: Frechet, but not Hadamard?

  • Testguy
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Graduate A question about the proof of the simple approximation lemma

  • Artusartos
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Lindelof Covering Theorem .... Apostol, Theorem 3.28 ....

  • Math Amateur
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Undergrad Lindelof Covering Theorem .... Apostol, Theorem 3.28 ....

  • Math Amateur
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Graduate Mapping of algebraic function to Riemann surface?

  • jackmell
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Graduate CW complex for infinite holed torus? (Surface of infinite genus)

  • dumbQuestion
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Graduate Topology: Munkres - Urysohn lemma

  • Fisicks
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Graduate Identifying Compact Sets in the Slitted and Moore Planes: What's the Method?

  • ForMyThunder
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Graduate Does SU(2) Commutativity Conflict with Its Non-Euclidean Structure?

  • Kontilera
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Graduate Is the Integral Inequality Possible to Prove for Certain Parameters?

  • amirmath
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Graduate Inquiry: Wavelet factorisation / Daubechies method /

  • MednataMiza
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Graduate Two definitions of locally compact

  • Fredrik
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Graduate How to Estimate the Operator Norm ||A||_2 for a Difference Operator?

  • Max Fleiss
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The Number e .... Another Question Regarding Sohrab Proposition 2.3.15 ....

  • Math Amateur
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Proposition 2.3.15: Understanding Sohrab's Basic Real Analysis Proof

  • Math Amateur
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Undergrad The Number e .... Sohrab Proposition 2.3.15 ....

  • Math Amateur
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Graduate Proof of the L'Hôpital Rule for the Indeterminate Form

  • 3.1415926535
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First Comparison Test for Series .... Sohrab Theorem 2.3.9 ....

  • Math Amateur
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Graduate Is it related to measure theory - Help

  • woundedtiger4
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Graduate The correct domain of self-adjointness for the Laplacian

  • AxiomOfChoice
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Graduate How to generalize Newtonian and Lagrangian mechanics

  • jostpuur
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Infinite Series .... Sohrab Exercise 2.3.10 (1) .... ....

  • Math Amateur
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Graduate Residue Proof of Fourier's Theorem Dirichlet Conditions

  • bolbteppa
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Graduate Question about bounded functions

  • pamparana
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Absolute and Conditional Convergence .... Sohrab Proposition 2.3.22 ....

  • Math Amateur
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Graduate Can the Fejér Kernel Be Approximated by Polynomials?

  • Vannel
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