Can we help you as soon as possible? Show that every closed subset of a compact space is compact but the converse neednot 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 finiteintersection property has non-empty intersection.

As per the guidelines I had given the proof of the first theorem. Kindly repost the another theorem…

Answered: a) Show that every closed subset of a…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 1TFE: Label each of the following statements as either true or false. The Well-Ordering Theorem implies...

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