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15
161
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A compact in a measurable set

Published on
#measure-theory #lebesgue-measure #compactness
543
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Image of countably compact space

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#general-topology #continuity #compactness
51
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Prove that a sequence of reals together with its limit is compact by cover

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#real-analysis #compactness
417
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$F$ closed, $K$ compact $\implies FK$ is closed in group $G$

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#general-topology #group-theory #compactness #topological-groups
227
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$F:X \to Y$ open continuous map when $X$ is Hausdorff and locally compact and $Y$ is Haussdorf

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#general-topology #compactness #open-map
489
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Is the set of all real symmetric matrices all of whose eigenvalues satisfy $|λ| \le 2 $ compact?

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#linear-algebra #general-topology #metric-spaces #compactness
143
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Two Hausdorff Compactifications are equivalent iff the sets of bounded continuous real valued functions in X which extend to Y and Z coincide.

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#general-topology #compactness
426
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Showing that intersection of arbitrarily many compact sets in Hausdorff space is compact.

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#general-topology #compactness #separation-axioms
135
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A wrong counterexample for the Sequential Compactness Theorem for general metric space?

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#metric-spaces #compactness #examples-counterexamples
54
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Prove that the given set is closed.

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#proof-verification #compactness
757
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$\epsilon$-ball in $X$ has compact closure. Show that $X$ is complete.

Published on
#compactness #cauchy-sequences #complete-spaces
273
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Continuous function in compact sets - Real analysis

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#real-analysis #functions #continuity #compactness
88
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Prove the following set is compact in $\mathbb{C}$

Published on
#complex-analysis #compactness #divergence-operator
274
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Intersection of compacts sets is compact "by open covering"

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#general-topology #compactness
57
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Show that two spaces are homeomorphic.

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#general-topology #metric-spaces #compactness #connectedness #complete-spaces

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