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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The Union of Two Open Sets is Open
- G-X
- · Replies 3 ·
Stromberg Theorem 3.47: why open set implies interval in intersection
- Math Amateur
- · Replies 2 ·
What are the V_k in Stromberg's theorem 3.43?
- Math Amateur
- · Replies 2 ·
TFAE proof involving limit and convergent sequence
- brooklysuse
- · Replies 2 ·
Undergrad Proving a Fixed Point Theorem for Shrinking Maps on Compact Spaces
- facenian
- · Replies 8 ·
High School Computing a tricky complex math problem - where did I go wrong?
- Mayhem
- · Replies 7 ·
Why is the Weierstrass function continuous but nowhere differentiable?
- mathmari
- · Replies 38 ·
Undergrad How do I create a sewing pattern for a spherical lune in 2D from an n-hosohedra?
- Smed
- · Replies 10 ·
Graduate Definitions of Cylinder Sets and Cylinder Set Measure
- leo.
- · Replies 2 ·
Undergrad Lindstrom Lemma 7.4.6: limit of integral over set B
- Math Amateur
- · Replies 6 ·
Lindstrom Lemma 7.4.6: proving the limit inequality for integrals
- Math Amateur
- · Replies 4 ·
Undergrad How do I separate the real and imaginary parts of an infinite product?
- benorin
- · Replies 5 ·
Undergrad Where is a list of Lehmer Pairs of zeros of zeta(s) ?
- Swamp Thing
- · Replies 2 ·
Undergrad Lindstrom Proposition 7.3.7: sum of measurable functions
- Math Amateur
- · Replies 14 ·
Lindstrom Proposition 7.3.7: sum of measurable functions
- Math Amateur
- · Replies 8 ·
Undergrad What's the name of a 2-torus looped in the 4th dimension?
- greswd
- · Replies 8 ·
Undergrad Do there exist surfaces whose boundary is a closed knot?
- jk22
- · Replies 3 ·
Undergrad Reference For The Historical Context of Dedekind Cuts and Why the need
- MidgetDwarf
- · Replies 8 ·
Prove Monotony of Function: $f$ Strictly Decreasing
- awsomeman
- · Replies 2 ·
Graduate Choosing a graduate complex analysis textbook
- benorin
- · Replies 23 ·
Undergrad Hölder and log-Hölder continuity
- hilbert2
- · Replies 2 ·
Undergrad Self teaching analysis and topology
- diegzumillo
- · Replies 9 ·
Undergrad Citation for a knot theory statement
- BillKet
- · Replies 3 ·
Linear isometry from R² to C in Garling example 11.5.2
- Math Amateur
- · Replies 2 ·
Proof of Corollary 11.4.3 in Garling's metric spaces book
- Math Amateur
- · Replies 2 ·
Graduate Nowhere diffferentable continuous function
- mathman
- · Replies 2 ·
Undergrad Proving Willard theorem 3.11 part 1-a using closure-interior duality
- Math Amateur
- · Replies 2 ·
Graduate How would you define a mathematical space?
- TheDS1337
- · Replies 11 ·
Annihilator of a set in Garling's metric spaces
- Math Amateur
- · Replies 2 ·
Proof that the annihilator satisfies both conjugate forms of the inner product
- Math Amateur
- · Replies 2 ·
Graduate Conformal Transformation as a diffeomorphism
- radioactive8
- · Replies 3 ·
Cauchy-Schwarz equality condition in Garling 11.3.2
- Math Amateur
- · Replies 2 ·
Graduate Proving that the real projective plane is not a boundary
- lavinia
- · Replies 38 ·
Is the Minimum of a Strictly Convex Function Unique at Its Critical Point?
- JS10
- · Replies 2 ·
Undergrad Proving X - E° = X - E closure in Willard
- Math Amateur
- · Replies 2 ·
Insights The Analytic Continuation of the Lerch and the Zeta Functions
- benorin
- · Replies 0 ·
Undergrad Is f(x) an Injective Function? Understanding Proof and Notation
- CaptainAmerica17
- · Replies 35 ·
Local extremum at ξ when f''(ξ) ≠ 0 and f'(ξ) = 0
- evinda
- · Replies 11 ·
Undergrad How does closure equality imply subset in Willard theorem 3.7?
- Math Amateur
- · Replies 5 ·
Undergrad Fractional Integral of which function is equal to Riemann's Zeta-Function?
- benorin
- · Replies 2 ·
Undergrad Reverse triangle inequality in Conway example 5.3.4(b)
- Math Amateur
- · Replies 2 ·
Undergrad Indiscrete topology generated by trivial pseudometric
- Math Amateur
- · Replies 6 ·
Open Sets in a Discrete Metric Space .... ....
- Math Amateur
- · Replies 2 ·
Equivalence classes of open sets in Willard Example 2.7(a)
- Math Amateur
- · Replies 3 ·
Undergrad Do Croom and Singh define local basis differently?
- Math Amateur
- · Replies 14 ·
Undergrad Explanation that sin(x+iy) is one-to-one
- hotvette
- · Replies 2 ·
Property of real-valued Fourier transformation
- mathmari
- · Replies 1 ·
Undergrad Finding a non-convergent Cauchy sequence
- Euler2718
- · Replies 10 ·
If f is convex and f(x) → ℓ, does f'(x) → 0?
- mathmari
- · Replies 23 ·
Undergrad Order topology basis in Singh's Elements of Topology 1.4.4
- Math Amateur
- · Replies 2 ·
Undergrad Coordinate Systems After Deformation of Axes
- Opus_723
- · Replies 2 ·
Show that the two functions are identical
- mathmari
- · Replies 4 ·
Undergrad Singh's description of topology generated by a subbasis
- Math Amateur
- · Replies 2 ·
Laplace transform of -3e^{9t}+9sin(9t)
- stephan2124
- · Replies 2 ·
Evaluating H(t-8)2cosh(t-8) with Heaviside function
- dean2203
- · Replies 2 ·
Undergrad Why does complement of exceptional terms guarantee eventual equality in Singh 4.1.1?
- Math Amateur
- · Replies 2 ·
Undergrad Why no rational is a limit of sequences in ℝ − ℚ
- Math Amateur
- · Replies 2 ·
Graduate Closure of constant function 1 on the complex set
- victorvmotti
- · Replies 11 ·
Undergrad Convergence of a sequence of sets
- benorin
- · Replies 44 ·
Undergrad Why does U in complement of A∪A' imply A∪A' is closed?
- Math Amateur
- · Replies 4 ·
Graduate Orthogonal complement of the orthogonal complement
- victorvmotti
- · Replies 4 ·
Undergrad Closed subsets vs. elements of a topological space
- Math Amateur
- · Replies 4 ·
Undergrad Can Intuition be Used in Mathematics to Overcome Limit Laws and Norms?
- Tucker121
- · Replies 3 ·
Undergrad Proving continuity definitions equivalent in Sutherland Chapter 8
- Math Amateur
- · Replies 2 ·
Undergrad Functional equations as global formulas
- Tendex
- · Replies 17 ·
Graduate Proof of Seifert-Van Kampen Theorem
- PsychonautQQ
- · Replies 2 ·
Why does f(x) < 0 for x between β and b in Silva's IVT proof?
- Math Amateur
- · Replies 3 ·
Graduate Questions about representation theory of Lie algebra
- phoenix95
- · Replies 5 ·
Undergrad Example of a Lie group that cannot be represented in matrix form?
- nrqed
- · Replies 18 ·
High School Something like an inverse Zeno's paradox
- archaic
- · Replies 11 ·
Undergrad Continuity at b implies f(t) > y in Browder 3.16
- Math Amateur
- · Replies 4 ·
Left continuity and the intermediate value theorem in Browder 3.16
- Math Amateur
- · Replies 2 ·
Undergrad Proving continuity of f+ = max(f, 0) at zeros of f
- Math Amateur
- · Replies 18 ·
Undergrad Why Isn't the Intersection of Two Lines a 1D Manifold?
- nrqed
- · Replies 21 ·
Continuity of f^+ = max(f, 0) where f crosses zero
- Math Amateur
- · Replies 4 ·
Relatively open sets in Stoll's Theorem 3.1.16
- Math Amateur
- · Replies 6 ·
Undergrad Why does f⁻¹(U) ∩ f⁻¹(J) = f⁻¹(U) in Browder 3.12?
- Math Amateur
- · Replies 5 ·
Undergrad Video lectures on lattices in mathematics
- senmeis
- · Replies 2 ·
Proving A ≤ f(t) ≤ B for increasing functions in Browder 3.7
- Math Amateur
- · Replies 3 ·
Undergrad Which class of functions does 1/x belong to?
- SVN
- · Replies 11 ·
Graduate Conditions to extend functions Continuously into the Boundary (D^1/S^1)
- WWGD
- · Replies 7 ·
Clarifying Conway's definition of continuity at a point
- Math Amateur
- · Replies 3 ·
Undergrad Conway's proof of Proposition 2.1.2 on function limits
- Math Amateur
- · Replies 7 ·
Undergrad Necessity condition in Browder theorem 5.10 on Riemann integrals
- Math Amateur
- · Replies 6 ·
Conway Proposition 3.1.4: uniqueness of the Riemann integral
- Math Amateur
- · Replies 2 ·
Differential of f(x,y) = (xy, x/y) using Browder proposition 8.12
- Math Amateur
- · Replies 2 ·
Browder's proposition 8.12 on differentials in R^n
- Math Amateur
- · Replies 2 ·
Undergrad Clenshaw-Curtis quadrature weights with even N collocation points
- confused_engineer
- · Replies 4 ·
Undergrad Application of the Stone Weierstrass Theorem
- CCMarie
- · Replies 9 ·
Partial fraction decomposition of a rational function with repeated poles
- lucad93
- · Replies 2 ·
Browder Proposition 8.14: Why does r(tv)/t approach zero as t→0?
- Math Amateur
- · Replies 2 ·
Why does Browder substitute h = tk in Definition 8.9?
- Math Amateur
- · Replies 2 ·
Undergrad The signal is binned into time bins with a width ##δt##
- arcTomato
- · Replies 4 ·
Understand Andrew Browder's Prop 8.13: Math Analysis Introduction
- Math Amateur
- · Replies 2 ·
Deriving f(p+h)−f(p)=Lh+r(h) from Browder's differentiability definition
- Math Amateur
- · Replies 2 ·
High School Can you determine the size of a manifold globally from its Euclidean embedding?
- sqljunkey
- · Replies 10 ·
Browder's remark on approximation by affine functions at a point
- Math Amateur
- · Replies 7 ·
Understanding Andrew Browder's Prop 8.7: Operator Norm and Sequences
- Math Amateur
- · Replies 4 ·
Understanding Proposition 8.7: Operator Norm and Sequences
- Math Amateur
- · Replies 4 ·
Operator Norm and Distance Function .... Browder, Proposition 8.6 ....
- Math Amateur
- · Replies 2 ·