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Convergence of sequence of functions in metric spaces

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#real-analysis #general-topology #convergence-divergence #metric-spaces
287
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What surface forms when you glue opposite sides of a rectangle together, introducing a half twist for both gluings?

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#general-topology
892
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The suspension (topology) and elementary examples

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#general-topology #manifolds #geometric-topology
53
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What are the limit points of set $E=\left\{ a_{n}\::\:n=1,\:2,\:3,\:\cdots\right\} $, $a_{n}=\frac{n-1}{n+1}\left|\sin\frac{n\pi}{7}\right|$

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#general-topology #limsup-and-liminf
143
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Inducing a sheaf on an open subset, or any subset?

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#general-topology #continuity #sheaf-theory #sheaf-cohomology
100
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Find really simple error in “proof” every subnet has a limit

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#general-topology #nets
75
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Help understanding this proof that $J$ is closed

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#general-topology #metric-spaces #proof-explanation
75
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On the nature of exotic spheres

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#general-topology #spheres
178
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Existence of an uncountable, pairwise disjoint collection of dense Borel sets, each of which is not in the algebra of open sets

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#real-analysis #general-topology #set-theory #cantor-set #borel-sets
293
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Topology containing a parabolic region

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#general-topology #problem-solving
681
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S is compact iff every continuous $ f: S \to \mathbb{R} $ has a maximum

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#general-topology #continuity #compactness
172
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Structure theorem for closed set in R

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#real-analysis #general-topology #analysis #proof-verification #metric-spaces
154
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Basic topology - Union property of topological spaces

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#general-topology #elementary-set-theory
78
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Implications of the Lebesgue covering lemma

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#general-topology #metric-spaces #compactness
422
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Uses of Cantors intersection theorem

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#general-topology #metric-spaces #proof-writing

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