Mathematics Homework Solutions
Problem
#35011

Continuity and Limit Points

1.  For i = 1,2 let fi: Xi --> Yi be maps between topological spaces. Show that the product f1Xf2: X1XX2 --> Y1XY2 defined by  f1Xf2(x1x2):= (f1(x1), f2(x2)) is continuous if and only if f1 and f2  are continuous.

*(Please see attachment for proper representation of formulas and problem #2)

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are continuous.

be a finite subset of the metric space (A,d). show that B has no limit
points.

Solution Summary

This is a proof regarding continuity and products.

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