show that lR is not compact!

Expert Solution

This is the right prove

-show that IR is not Compact. Compact space.- - A topological space is Compeich If every open comes of has sinulle subcoves. Assume IR is compact Let 0 = 2 Uning = {(1, n?n21 be open cover of R. Conside ginine subcomis { uinte f Con=l, mas N= max kn, z . nas we get that In CUN & Un; = IN (N-), N+1) ÇIR Flence ous O cannot beans a finite assum. conany Sablonen. 7 IR is not corpaes.

Colby Messinger answered 2 years ago

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