a) Show that every closed subset of a compact space is compact but the converse need not to be true ..

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Show that every closed subset of a compact space is compact but the converse need
not to be true ..
(b) Show that every compact of T2-space is t4-space.
(c) Show that a space X is compact iff for any family of closed sets which satisfy finite
intersection property has non-empty intersection.
Transcribed Image Text:Show that every closed subset of a compact space is compact but the converse need not to be true .. (b) Show that every compact of T2-space is t4-space. (c) Show that a space X is compact iff for any family of closed sets which satisfy finite intersection property has non-empty intersection.
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