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Every nonempty perfect set in $\mathbb R^k$ is uncountable: Rudin's argument

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#real-analysis #general-topology #compactness
846
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Help in understanding proof of Heine-Borel Theorem from Simmons

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#general-topology #metric-spaces #compactness
164
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Is the distance between those compact sets equal to $0$?

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#general-topology #elementary-set-theory #metric-spaces #compactness
64
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Are compact groups acting on Polish spaces essentially Polish?

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#general-topology #compactness #topological-groups #descriptive-set-theory #polish-groups
191
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Set of Positive Sequences that Sum to 1 is Compact under Product Topology?

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#general-topology #compactness #product-space #weak-topology
103
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The space $D(A^\infty)$

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#functional-analysis #operator-theory #hilbert-spaces #compactness #compact-operators
974
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Proving the one-point compactification of a topological space is a topology

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#general-topology #proof-verification #compactness #compactification
170
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Never Used Compact Closure...

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#general-topology #compactness
72
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Continuity of the maximal element of a multi-valued function

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#functional-analysis #continuity #compactness #multivalued-functions
1.1k
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Consider the metric space of infinite sequences of 0s and 1s under this metric.

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#real-analysis #sequences-and-series #metric-spaces #compactness
171
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Sequence in $B[0,1]\subset L^2[0,1]$ which has no convergent subseqence.

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#general-topology #functional-analysis #compactness #lp-spaces
243
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Weakly sequentially continuous maps

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#functional-analysis #operator-theory #compactness #sobolev-spaces #compact-operators
938
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Why are functions of compact support so important?

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#general-topology #functional-analysis #compactness #intuition
551
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Weak and strong compactness in $L^2$

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#compactness #lp-spaces #weak-convergence
668
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Compact sets in uniform norm

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#normed-spaces #compactness #lipschitz-functions

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