'Finite open cover' presentation slideshows

Continuous functions

Continuous functions. Definition: Let f be a function from a metric space (X,d1) to a metric space (Y,d2) then we say that f is a continuous function at x=a if : for each open set G in Y such that f(a) ? G, then f -1 (G) is open set in X. f is continuous if it continuous at all a? X. Example:

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