On compactification of metric spaces
Tóm tắt
Iff:X →X* is a homeomorphism of a metric separable spaceX into a compact metric spaceX* such thatf(X)=X*, then the pair (f,X*) is called a metric compactification ofX. An absoluteG
δ-space (F
σ-space)X is said to be of the first kind, if there exists a metric compactification (f,X*) ofX such that
$$f(X) = \mathop \cap \limits_{i = 1}^\infty G_i $$
, whereG
i are sets open inX* and dim[Fr(G
i)]
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