Math Analysis question: Please determine compactness and connectedness of the following set in R: Please briefly explain why. Solution by a known theorem ,A subspace of a real line is connected if and only if it is an interval. therefore A is connected in extended real line. By Heine-Borel theorem, Every closed and bounded subspace of real line is compact, therefore A is compact in exteneded real line. if R =(-inf,inf) open interval then A is not subset of R. both are not happen.

1. Math Analysis question:
Please determine compactness and connectedness of the following set in R:
Please briefly explain why.
Solution
by a known theorem ,A subspace of a real line is connected if and only if it is an interval.
therefore A is connected in extended real line.
By Heine-Borel theorem, Every closed and bounded subspace of real line is compact,
therefore A is compact in exteneded real line.
if R =(-inf,inf) open interval then A is not subset of R. both are not happen