A subspace of a space such that for every neighbourhood of it in there is a set that is the union of a countable family of sets closed in and with . If is normally imbedded in and is normally imbedded in , then is normally imbedded in . A normally-imbedded subspace of a normal space is itself normal in the induced topology, which explains the name. Final compactness of a space is equivalent to its being normally imbedded in some (and hence in any) compactification of this space. Quite generally, a normally-imbedded subspace of a finally-compact space is itself finally compact.
|||Yu.M. Smirnov, "On normally-imbedded sets of normal spaces" Mat. Sb. , 29 (1951) pp. 173–176 (In Russian)|
A finally-compact space is the same as a Lindelöf space.
Normally-imbedded subspace. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normally-imbedded_subspace&oldid=11245