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From Encyclopedia of Mathematics
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of a set under a mapping

The set of all for which . An equivalent definition is: . Closed and irreducible mappings may be characterized by means of small images. A continuous mapping is closed (cf. Closed mapping) if and only if the small image of each open set is open. A continuous mapping onto is closed and irreducible (cf. Irreducible mapping) if and only if the small image of each non-empty open set is a non-empty set.

How to Cite This Entry:
Small image. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Small_image&oldid=48735
This article was adapted from an original article by V.V. Fedorchuk (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article