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15
577
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$X \subset \mathbb{R}^n$ bounded $\implies f(X)$ is Bounded

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#continuity #compactness
28
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Characterizing properties of the given set (regression coefficient). Is it convex? Does it have holes? Is it compact?

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#real-analysis #general-topology #convex-analysis #compactness #connectedness
182
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Baby Rudin Theorem 2.34

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#metric-spaces #compactness
85
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Suppose a subspace of $X$ is compact iff closed. Then is $X$ compact hausdorff?

Published on
#general-topology #compactness #separation-axioms
496
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Fredholm’s alternative

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#functional-analysis #operator-theory #compactness #compact-operators
203
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Sequential compactness of unit ball in $B(X)$

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#general-topology #functional-analysis #operator-theory #compactness
203
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Is $\{0,1\}^{\mathbb{N}}$ compact in $\mathbb{N}^{\mathbb{N}}$?

Published on
#compactness
867
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Continuos functions with compact support on a closed interval

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#functional-analysis #compactness
75
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A stronger form of pseudo-compactness.

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#general-topology #compactness
585
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Is the set $E$ is open, closed, compact in $\mathbb{Q}$

Published on
#real-analysis #metric-spaces #compactness
310
Views

upper bound of outer measure on compact support of continuous function

Published on
#measure-theory #compactness #outer-measure #borel-measures
99
Views

Showing compactness of an operator

Published on
#compactness #sobolev-spaces #lp-spaces #calculus-of-variations #compact-operators
115
Views

Semi-norms and Hausdorff compact convex set in locally convex space

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#functional-analysis #compactness #locally-convex-spaces
76
Views

Is $\{0,1\}^{\mathbb{N}} \setminus \{(x_n)_n \in \{0,1\}^{\mathbb{N}} \mid x_n=1\: \text{for almost all} \: n \in \mathbb{N}\}$ compact?

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#general-topology #compactness
1.7k
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An analytic function in a compact region has finitely many zeros

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#complex-analysis #compactness #analytic-functions

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