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Find the supremeum and infimum, and is the set compact?

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#real-analysis #general-topology #compactness #supremum-and-infimum
136
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Is the following number set compact?

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#real-analysis #compactness
269
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prove the following lemma about a compact space and a ultrametric.

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#general-topology #metric-spaces #compactness #ultrametric
359
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A first countable hemicompact space is locally compact

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#general-topology #compactness #first-countable
151
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To check whether given space is metrizable

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#general-topology #metric-spaces #compactness #metrizability
101
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Locally compact metric space having atleast one non-compact closed ball

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#metric-spaces #compactness #normed-spaces
228
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Covering and Heine-Borel theorem

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#general-topology #complex-analysis #compactness
1.7k
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Compactness of a metric space

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#real-analysis #general-topology #metric-spaces #compactness #complete-spaces
73
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Let $C$ be compact sets. $\bigcap_{i \in K} (C_i)=\emptyset \Rightarrow \exists F \subseteq K \; \text {finite} | \bigcap_{i \in F} (C_i) = \emptyset$

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#general-topology #compactness #fake-proofs
50
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How i can show that this set is compact?

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#general-topology #analysis #metric-spaces #compactness
101
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Clarification on locally compact space

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#real-analysis #general-topology #compactness
465
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Let $S$ be a nonempty subset of $\mathbb{R}$. If ܵS is a finite union of disjoint bounded intervals, then which one of the following is true?

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#real-analysis #compactness
611
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Number of connected components of a set.

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#general-topology #compactness #connectedness
555
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Compactness of $\{x \rightarrow \sin(\pi nx) : n \in \mathbb{Z}\}$

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#real-analysis #compactness
113
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Compactness of $\ A= \{f: f$ is power series with infinite radius of convergence and is bounded by $1\}$

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#real-analysis #compactness

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