Characterizing continuous functions in terms of separated sets: International Journal of Mathematical Education in Science and Technology: Vol 36, No 5

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Abstract

The following theorem is proved: let f:X →Y and suppose points are closed in Y (that is, singleton sets are closed in Y). Then, f is continous if and only if f ¹ preserves separated sets. We also give a counter example in the event points are not closed in Y.

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Characterizing continuous functions in terms of separated sets

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Characterizing continuous functions in terms of separated sets

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