Lattice-valued convergence spaces and regularity

Jäger, G. (2008) Lattice-valued convergence spaces and regularity. Fuzzy Sets and Systems, 159 (19). pp. 2488-2502. ISSN 0165-0114

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Official URL: http://dx.doi.org/10.1016/j.fss.2008.05.014

Abstract

We define a regularity axiom for lattice-valued convergence spaces where the lattice is a complete Heyting algebra. To this end, we generalize the characterization of regularity by a ”dual form” of a diagonal condition. We show that our axiom ensures that a regular T1-space is separated and that regularity is preserved under initial constructions. Further we present an extension theorem for a continuous mapping from a subspace to a regular space. A characterization in the restricted case that the lattice is a complete Boolean algebra in terms of the closure of an L-filter is given.

Item Type:Article
Uncontrolled Keywords:L-fuzzy convergence; L-topology; L-filter; L-diagonal filter; L-convergence space; pretopological space; diagonal condition; regularity; T1-axiom; T2-axiom; dense subset; continuous extension.
Subjects:Y Unknown > Subjects to be assigned
Divisions:Faculty > Faculty of Commerce > Statistics
Faculty > Faculty of Science > Statistics
ID Code:1255
Deposited By: Mrs Eileen Shepherd
Deposited On:11 Nov 2008
Last Modified:06 Jan 2012 16:20
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