8- Let X, Y are metric spaces and f: X → Y .If for any A C X, f(A) C f(A) then f is continuous.

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7- In R with the usual metric, R+ has only one lower bound.
8- Let X, Y are metric spaces and f X → Y .If for any A C X,
f(A) C f(A) then f is continuous.
9- For any closed set A in a metric space, A = A.
10- In any complete metric space, every Caushy sequence is convergent.
Transcribed Image Text:7- In R with the usual metric, R+ has only one lower bound. 8- Let X, Y are metric spaces and f X → Y .If for any A C X, f(A) C f(A) then f is continuous. 9- For any closed set A in a metric space, A = A. 10- In any complete metric space, every Caushy sequence is convergent.
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