Extensions defined using bornologies

Alessandro Caterino

Italy

Università degli Studi di Perugia

Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123, Perugia, Italy.

M. Cristina Vipera

Italy

Università degli Studi di Perugia

Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123, Perugia, Italy.

Submitted: 2013-07-31

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Accepted: 2013-07-31

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Published: 2013-07-31

DOI: https://doi.org/10.4995/agt.2011.1644
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Keywords:

Boundedness, Bornology, Topological extension, B-extension

Supporting agencies:

This research was not funded

Abstract:

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.
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