Many extensions of a space X such that the remainder Y is closed can be constructed as B-extensions, that is, by defining a topology on the disjoint union X [ Y , provided there exists a map, satisfying some conditions, from a basis of Y into the family of the subsets of X which are “unbounded” with respect to a given bornology in X. We give a first example of a (nonregular) extension with closed remainder which cannot be obtained as B-extension. Extensions with closed discrete remainders and extensions whose remainders are retract are mostly considered. We answer some open questions about separation properties and metrizability of B-extensions.
Boundedness; Bornology; Topological extension; B-extension