almost locally compact

almost locally compact

Definition

Let X be a topological space and A a subspace of X.
τ(A,X) denotes the family of all open sets in X which contain A. A subfamily B of τ(A,X) is called an outer base if for all U in τ(A,X) there is some V in B included in U.
X is called almost locally compact if the set of all points at which X is not locally compact is contained in a compact set with countable outer character.

Reference

D. Jardon and V. V. Tkachuk, Ultracomplete metaLindelof spaces are almost locally compact, New Zealand J. Math. Vol. 36, pp.277-285 (2007).