Compactness Def Lemma&Theorem In Finite Dimensional Normed Space M⊂X Compact iff M is closed&Bounded
Lecture #44 • Functional analysis(Erwin kreyszing)Chapte... Lecture#47 Section#2.5 Compactness in Normed Space Defination: Compact Space OR Sequentially Compact Lemma: A Compact Subset M of a Metric Space.is Closed & Bounded.The converse of this lemma is not true. Theorem: In a Finite Dimensional Normed Space X.any Subset M⊂X is Compact if and only if M is closed and Bounded
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In finite dimensional Normed space a subset M is compact iff it is closed and bounded
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