Question: n lecture i said that iffxyis a function between metric spaces, ifxx1x2 xnis a finite cover ofxby closed sets, and iffis continuous on eachxi, thenfis

n lecture i said that iffxyis a function between metric spaces, ifxx1x2 xnis a finite cover ofxby closed sets, and iffis continuous on eachxi, thenfis continuousonx prove this statement (if you want a few extra extra points, prove that it is not alwaystrue for infinite closed covers)

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