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The distance from a point to a union of sets is the infimum of the distances

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#general-topology #metric-spaces
55
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Continuity of a function $f:X \longrightarrow Y$ Where $X,Y$ metric space

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#real-analysis #metric-spaces
197
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Equivalent definition of "totally boundedness"

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#general-topology #metric-spaces
70
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Example of a non-surjective isometric mapping on a totally bounded metric space

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#general-topology #metric-spaces #compactness #isometry
53
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Path connectedness of a subset of $\mathbb{R}^2$

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#general-topology #metric-spaces
59
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$(E\cup F)' = E' \cup F'$

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#analysis #metric-spaces
342
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Understanding a Proof: The square root of any metric is ptolemaic..

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#inequality #metric-spaces #geometric-inequalities #metric-geometry
46
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Contraction Mapping with uniform metric...

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#real-analysis #analysis #metric-spaces
137
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Two metric spaces X and Y being isometric implies group of isometries are isomorphic

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#general-topology #metric-spaces #group-isomorphism #isometry
225
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What is the relative interior of this set?

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#general-topology #multivariable-calculus #optimization #metric-spaces
44
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Continuity of supremum with respect to the metric of coordinatewise convergence

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#general-topology #metric-spaces
406
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Topological spaces which are not pseudometrizable.

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#general-topology #metric-spaces #examples-counterexamples
290
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Compactness via closed sets

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#general-topology #metric-spaces
100
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Ball around a set equals union of balls around each of its points

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#real-analysis #general-topology #metric-spaces
43
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Prove function is a metric

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#real-analysis #metric-spaces

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