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Continuous function on a compact set with no fixed points

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#analysis #continuity #compactness
28
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Proving compactness in a geometric scenario

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#proof-verification #metric-spaces #compactness
1k
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Is the trace set of orthogonal matrix compact?

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#linear-algebra #matrices #compactness #trace #orthogonal-matrices
409
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Compactness is independent of the ambient space

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#real-analysis #general-topology #compactness
52
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Can someone formalize 'compactness of set' defined as follows?

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#analysis #compactness
136
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Show that $\hat{E}\setminus E$ is homeomorphic to $S^1$

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#general-topology #compactness
92
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Open sets in locally compact spaces

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#general-topology #compactness
39
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How do we call such a compactification?

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#general-topology #compactness
403
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non-symmetric version of compact = totally bounded + complete

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#general-topology #metric-spaces #compactness #uniform-spaces
378
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Regularity of Dirac measure on Baire sets

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#real-analysis #general-topology #measure-theory #compactness
1.8k
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Check if the given set is Connected and Compact.

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#general-topology #metric-spaces #compactness #connectedness
38
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Show compactness of $E\cup S_1$

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#compactness
627
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Compact Connected Hausdorff Space has no compact component in the complement of a point

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#general-topology #compactness #connectedness
306
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Complement of a point of a Compact Connected Hausdorff Space has no compact maximal connected subspace

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#general-topology #compactness #connectedness
103
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Metric $p := p(x,y)= \min(|x-y|, 1- |x-y|)$ $x,y \in [0,1)^2$. Prove metric space is compact.

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#sequences-and-series #metric-spaces #compactness

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