Hi,

can anyone help me ?

Given Topological Spaces (metric spaces)(X, d1)and(Y,d2), show that a function

f: X -> Yis continuous if and only iff(cl of A)is a subset ofcl of f(A)for all A subset X1.

How can i proof this ?

Thank you!!!

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- Nov 8th 2011, 05:34 AMMajrouContinuity and closure
Hi,

can anyone help me ?

Given Topological Spaces (metric spaces)**(X, d1)**and**(Y,d2)**, show that a function

**f: X -> Y**is continuous if and only if**f(cl of A)**is a subset of**cl of f(A)**for all A subset X1.

How can i proof this ?

Thank you!!! - Nov 8th 2011, 05:58 AMgirdavRe: Continuity and closure
Remember that if $\displaystyle f$ is a function defined on a metric space, then $\displaystyle f $ is continuous if and only if $\displaystyle \{f(x_n)\}$ converges to $\displaystyle f(x)$ whenever $\displaystyle \{x_n\}$ converges to $\displaystyle x$.