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15
161
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Example: limit point compact + $\neg$countably compact+ $\neg$Lindelöf

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#general-topology #compactness #examples-counterexamples
111
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Continuity Proof "If $f(x,w)$ is continuous and its domain is a cartesian product, $\max_{w}f(x,w)$ is continuous."

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#continuity #convex-analysis #compactness #maxima-minima
301
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Unitary Representations and the Peter-Weyl Theorem

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#analysis #representation-theory #compactness #topological-groups
439
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Properties of topological vector spaces

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#general-topology #compactness #intuition #topological-vector-spaces #locally-convex-spaces
142
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Find a sequence of functions $\{g_n\}$ in $C([0,1])$ so that $\overline{\{g_n\}}$ is compact, but $g_n$ does not converge uniformly.

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#real-analysis #compactness #uniform-convergence
51
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Suppose $f:[0,1]\times[0,1]\mapsto X$ is a continuous function. Show that $[0,1]\times[0,1]$ can partitioned into rectangles s.t $f(R_i)\subseteq U_k$

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#general-topology #compactness #cauchy-sequences
160
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Berkeley Problem 4.1.11 Incorrect Proof in Answer Key?

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#real-analysis #metric-spaces #compactness
570
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Finitely sheeted covering space of a compact space is compact

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#general-topology #compactness #covering-spaces
44
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Metric space compactness

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#analysis #metric-spaces #compactness
121
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Showing $f(B_r)$ is relatively compact for a certain $f$.

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#general-topology #functional-analysis #metric-spaces #compactness #normed-spaces
44
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A linear topological space over real number field is locally compact ???

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#general-topology #vector-spaces #compactness #topological-vector-spaces #locally-compact-groups
43
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Continuity of a function and its consequences

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#limits #continuity #compactness #uniform-continuity
46
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Compactness of Sobolev Space

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#sequences-and-series #functional-analysis #compactness #sobolev-spaces
160
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Problem about components in a compact Hausdorff space

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#general-topology #compactness #equivalence-relations
47
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On compactness in open sets

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#real-analysis #general-topology #compactness

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