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Characterizing continuous functions in terms of separated sets |
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| Authors: | Mark Lynch |
| Institution: | University of Oldenburg , Federal Republic of Germany |
| 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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