TY - JOUR
AU - Caterino, Alessandro
AU - Vipera, M. Cristina
PY - 2013/07/31
Y2 - 2024/05/28
TI - Extensions defined using bornologies
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 12
IS - 2
SE -
DO - 10.4995/agt.2011.1644
UR - https://polipapers.upv.es/index.php/AGT/article/view/1644
SP - 81-94
AB - 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.
ER -