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The "Circle" is a Vector Space?

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#analysis #functional-analysis #vector-spaces #metric-spaces #circles
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If $A$ and $B$ are closed subsets of the set of real numbers, then is $A+B$ closed?

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#metric-spaces
74
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Does a strictly convex and weak metrizable unit sphere of a Banach space imply separability?

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#functional-analysis #metric-spaces
257
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Connected subsets of metric (or T1) spaces

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#general-topology #metric-spaces #connectedness
1k
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When a group acts on a metric space isometrically, transitively, and faithfully, is it a closed subspace of the isometry group?

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#group-theory #metric-spaces #topological-groups
84
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Proving that a function on a compact metric space is bounded above

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#real-analysis #metric-spaces
1.1k
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Topological spaces vs. metric spaces

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#general-topology #metric-spaces
438
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Two definitions of compact set

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#real-analysis #metric-spaces #compactness
76
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Different metric structure on $\mathbb{Z}$

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#metric-spaces
1.1k
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How to make the Symmetric Distance a metric?

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#geometry #metric-spaces
658
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Bounded metric on $\mathbb{R}$

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#real-analysis #metric-spaces
405
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distance metric between multisets

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#metric-spaces #multisets
1k
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Rudin's Topological Definition of an Open Set -- Does it Disagree with the Metric Space Definition?

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#general-topology #metric-spaces
155
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Tails sets are Borel

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#real-analysis #probability #measure-theory #elementary-set-theory #metric-spaces
109
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convergence of a sequence of cauchy

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#real-analysis #sequences-and-series #analysis #metric-spaces #cauchy-sequences

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