RESULTS ON OPEN & CLOSED SETS -1 #results #open #& #closed #sets
https://youtu.be/-Z7sRAcTBRs?si=ezkfp_zlrrINstER
RESULTS ON OPEN SET:
Result : A subset G of a metric space X is open iff it is a union of open spheres.
proof :
R Result . Let X be a metric space. Then
i. Any union of open sets in X is open in X and
ii. Any finite intersection of open sets in X is open in X.
Result : In any metric space X, every closed sphere is a closed set.
#results #open #& #closed #sets
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