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Bifactorial mapping

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A mapping $f$ of a topological space $X$ into a topological space $Y$, in which for any covering of the inverse image $f^{-1}(y)$ of any point $y\in f(X)$ by sets open in $X$ it is possible to select a finite number of sets so that $y$ is located inside the image of their union. It is particularly important that the product of any collection of bifactorial mappings is a bifactorial mapping. Bifactorial mappings constitute an extensive class of factorial mappings, but nevertheless preserve the fine topological properties of spaces. Thus, continuous bifactorial $s$-mappings preserve a pointwise-countable base, and a factorial $s$-mapping of a space with a pointwise-countable base onto a space of pointwise-countable type is bifactorial.

How to Cite This Entry:
Bifactorial mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bifactorial_mapping&oldid=31588
This article was adapted from an original article by V.V. Filippov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article