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- W1989729302 abstract "Let f:X→Y be continuous where X is a topological space and Y a metric space. Given a set E⊂Y, we ask whether f admits arbitrarily close continuous approximations whose values omit E (see Definition 2). It is shown that if X is paracompact, dimX⩽k, then each continuous mapping X→Rn, n>k, has an arbitrarily close approximation avoiding the product of n given boundary subsets of R. Also, we discuss a related topic consisting in finding conditions under which the approximating mappings do not take values in certain balls. In this connection, we investigate relations between the accuracy of approximations and the radii of omitted balls." @default.
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- W1989729302 date "2011-06-01" @default.
- W1989729302 modified "2023-10-18" @default.
- W1989729302 title "On some properties of approximations" @default.
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- W1989729302 doi "https://doi.org/10.1016/j.topol.2011.03.010" @default.
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