Abstract:There are theorems in which some classes of topological spaces are
characterized by means of properties of mappings of these spaces into a single
space. For example, it is well known that a compactum X
is at most n-dimensional if and only if no mapping of X
irto an (n + l)-cube has a stable value [5, Theorems
VI. 1-2, pp. 75-77]. Also, a curve X is tree-like if
and only if no mapping of X into a figure e… Show more
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