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Are the three notions of compactness equivalent for uniform spaces?

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#general-topology #compactness #examples-counterexamples #separation-axioms #uniform-spaces
139
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How to determine number of genus from given equation of a surface?

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#general-topology #algebraic-topology #surfaces
86
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How to find paths in the graph with strong links?

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#general-topology #graph-theory #optimization #linear-programming
109
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How to define topologies on different Banach spaces

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#general-topology #functional-analysis
1.2k
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Can a set of positive measure and its complement both have empty interior?

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#general-topology #measure-theory #examples-counterexamples #cantor-set
748
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Prove that if for $E$ and $F$ connected sets, if $E \cap F \neq \emptyset \rightarrow E \cup F$ is connected

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#real-analysis #general-topology #metric-spaces
64
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Spaces for which invariance of domain holds

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#general-topology #algebraic-topology
216
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If $d(x,y)$ is a metric on $X$, then $d'(x,y)=\frac{d(x,y)}{1 + d(x,y)}$ and $d(x,y)$ generates the same topology.

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#general-topology #proof-verification #metric-spaces
1.2k
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Proving the cofinite topology is coarser then the Euclidean topology.

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#real-analysis #general-topology #proof-verification #proof-writing
242
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Prove that the polar set of a convex set contains the origin

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#general-topology #convex-analysis #polytopes
389
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Intuition Behind Whitney Covering Lemma

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#real-analysis #general-topology
660
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Open connected subsets of path connected spaces

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#general-topology #metric-spaces #examples-counterexamples #connectedness #path-connected
291
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semi-direct product between manifolds

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#general-topology #manifolds #geometric-topology #fiber-bundles #surgery-theory
82
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Differentiability of $a:K\to \mathcal{B}(E,F)$?

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#real-analysis #general-topology #functional-analysis #operator-theory #banach-spaces
65
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Basis of topological space

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#general-topology

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