Lattice-valued convergence spaces and regularity

Title: Lattice-valued convergence spaces and regularity
Creator: Jäger, Gunter
Date: 2008
Type: text
Type: Article
Identifier: vital:6826
Identifier: http://hdl.handle.net/10962/d1012336
Description: 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.
Format: 22 pages, pdf
Language: English
Relation: Jäger, G. (2008) Lattice-valued convergence spaces and regularity. Fuzzy Sets and Systems, 159 (19). pp. 2488-2502. ISSN 0165-0114. Available: http://dx.doi.org/10.1016/j.fss.2008.05.014
Rights: Jäger, G

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