Extensions defined using bornologies

Authors

  • Alessandro Caterino Università degli Studi di Perugia
  • M. Cristina Vipera Università degli Studi di Perugia

DOI:

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

Keywords:

Boundedness, Bornology, Topological extension, B-extension

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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Author Biographies

Alessandro Caterino, Università degli Studi di Perugia

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

M. Cristina Vipera, Università degli Studi di Perugia

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

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Published

2013-07-31

How to Cite

[1]
A. Caterino and M. C. Vipera, “Extensions defined using bornologies”, Appl. Gen. Topol., vol. 12, no. 2, pp. 81–94, Jul. 2013.

Issue

Section

Regular Articles