Question

Let I©R be compact and continuous then what will that function is definitely will be?​

Answer 1

Answer:

Here A is the index set and may be finite, countably or uncountably infinite.

Definition 3.8

K⊂X is compact if any open cover of K has a finite subcover. More explicitly, K is compact if whenever K⊂∪α∈AGα, where each Gα is open, there exists a finite number of indices α1,α2,…,αm∈A such that K⊂∪

m

j=1

Gαj. In addition, E⊂X is precompact (or relatively compact) if

¯

E

is compact. If X is a compact set, considered as a subset of itself, then we say X is a compact metric space.