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.
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Insights The Orin Fractional Calculus
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Undergrad About the definition of topological manifold using closed sets
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Undergrad Apparent counterexample to Cauchy-Goursat theorem (Complex Analysis)
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Undergrad 2-sphere intrinsic definition by gluing disks' boundaries
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Undergrad Confused by proof in Hocking and Young
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Undergrad "Magic" regulating functions for divergent series
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Undergrad How are the following three definitions subtly different?
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Undergrad Evaluate two complex integrals along a parabolic contour
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Undergrad Convergence not defined by any metric
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Undergrad Homemorphism in quotient topology
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Undergrad No structure in ##(d,x)## in ##\textbf{Met*}(X)## is admissible
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Undergrad A beginner’s thoughts on rotation number -- Resource suggestion request
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Insights The Many Faces of Topology
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Undergrad What is the 4D Equivalent of a Möbius Strip or Klein Bottle?
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Undergrad In Which N-Dimensional Spaces Are Rotations Chiral?
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High School Functions f: ℝ --> ℝ
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Undergrad Continuity of linear map from subspace of Euclidean space
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Undergrad Uniform convergence of difference quotient in higher dimensions
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Graduate A complicated integral to be evaluated by complex contour method
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Undergrad Dyadic cubes generate Borel sigma algebra of subset
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High School Topological neigborhoods that are not intervals in the real line?
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Undergrad Homeomorphism onto a not open image in the target
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Undergrad On commutativity of convolution
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Undergrad A concise "proof" of the Riemann-Lebesgue lemma
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Undergrad A curve that does not meet rational points
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Undergrad About convergence of complex power series on the circle ##|z - z_0|=r##
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Graduate Information theory via knot theory
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Undergrad Connection between absolute continuity of function and measure
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Undergrad Pointwise convergence in Lp space
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Undergrad Norm of integral less than or equal to integral of norm of function
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High School Continuity of ln(x) function
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Undergrad How to show the diagonal in the extended plane is closed?
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Undergrad Verifying pointwise convergence of indicator functions
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Undergrad Measure with respect to complete measure is also complete
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Undergrad Help understanding a passage from a proof of change of variables formula
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Undergrad Metric Tensor on ##S^1## x ##S^2##
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Undergrad Unit sphere is compact in 1-norm
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Undergrad Exercise 2.23 in Folland's real analysis text
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Undergrad Does Ricci Flow Contract a 3-Sphere to Its Center?
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Undergrad On translation and dilation invariant Lebesgue measure: Folland's text
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Undergrad Simple partitioning of sequence in Proposition 1.15 in Folland's text
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Undergrad Regarding dominated convergence theorem in Folland
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Undergrad On Borel sets of the extended reals
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Undergrad Basic question on 'bounded implies totally bounded'
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Undergrad Open balls dense in closed balls in Euclidean space
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Undergrad Show that a "cross" is not a topological manifold
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Undergrad Tough lemma on locally finite refinement
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Graduate Cubical cup poduct with a unit 1-cochain and the coboundary operator
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Undergrad Compact support functions and law of a random variable
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Undergrad Uniform closure of algebra of bounded functions is uniformly closed
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Undergrad Parallel rectangles contained in oblique rectangle
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Graduate Question about different statements of Picard Theorem
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Undergrad Question about convex property in Jensen's inequality
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Undergrad A non-empty intersection of closures of level sets implies discontinuity
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Graduate Proving that this integral is divergent
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Graduate Question about covering map of punctured unit disk
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Graduate Question about lifting of a function
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Graduate Question about existence of path-lifting property
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Undergrad Riemann integrability and uniform convergence
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MHB Integration in Polar Coordinates (Fubini/Tonelli)
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Undergrad On theorem 1.19 in Folland's and completion of measure
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Undergrad Are slices of measurable functions measurable?
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Undergrad On integral of simple function and representation
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Undergrad Collection of finite unions of half-open intervals form an algebra
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Undergrad How Does the Hopf Map Relate to Foliation and Knot Theory on the 3-Torus?
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Undergrad Help with basic transfinite induction proof
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Undergrad On two definitions of locally compact
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Undergrad Showing equivalence of two definitions of essential supremum
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Undergrad Two basic results from measure theory -- on volumes of rectangles
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Undergrad In which sense(s) do square integrable functions go to zero at infinity?
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Graduate Functional Analysis for Physics in 2024
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Undergrad Question about branch of logarithms
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Undergrad Verify the completion of continuous compactly supported functions
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Undergrad Fiber bundle homeomorphism with the fiber
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Undergrad On deriving the (inverse) Fourier transform from Fourier series
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Undergrad Prove projection of a measurable set from product space is measurable
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High School Questions on a numberphile video
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Undergrad ##SU(2, \mathbb C)## parametrization using Euler angles
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Undergrad Regarding Wirtinger's inequality
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Undergrad ##SL(2,\mathbb R)## Lie group as manifold
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Undergrad Is the Projection Restriction to a Linear Subspace a Homeomorphism?
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Undergrad New Video Course on General Topology on YouTube
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Undergrad ##SU(2)## homeomorphic with ##\mathbb S^3##
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Undergrad Bloch Analysis proof of Theorem 2.5.5 (Definition by recursion)
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Undergrad How do I use the four axioms of a neighborhood to define an open set?
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Undergrad How to define an open set using the four axioms of a neighborhood
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Undergrad Is the Belt Trick Possible with Continuous Deformation in 3D Rotation Space?
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Undergrad On differentiability and Fourier coefficients (Vretblad's text)
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Graduate Complex analysis -- Essential singularity
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Undergrad On limit of convolution of function with a summability kernel
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Undergrad Fourier coefficients of convolution
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Undergrad Outer measure .... Axler, Result 2.14 .... Another Question ....
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Undergrad Bounding modulus of complex logarithm times complex power function
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High School Confusion with the basics of Topology (Poincare conjecture)
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Undergrad Is a Locally One-to-One Proper Map Globally Bijective?
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Undergrad On a remark regarding the Cauchy integral formula
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Undergrad Infinity Numbers (Expanded P-Adic Numbers)
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Undergrad Why is this function not ##L^1(\mathbb{R} \times \mathbb{R})##?
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High School Why is the set {(x,y)∈Ω×R|y=f(x)} a manifold?
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Graduate Topology - Boundary of a ball without a point
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Undergrad Feedback for my YouTube Videos on Real Analysis
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