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!!!
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!!!
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 $\displaystyle x$.