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24th Summer Conference on Topology and Its Applications
July 14-17, 2009
Faculty of Electrical Engineering and Communication, Brno University of Technology
Brno, Czech Republic

Organizers
Josef Šlapal (chair), Martin Kovár, Jan Paseka, Miroslav Kureš

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Partial Metrics and Fuzzy Equalities
by
Michael Bukatin
MetaCarta, Inc., Cambridge, Massachusetts, USA
Coauthors: R.Kopperman, S.Matthews, and H.Pajoohesh

Partial metrics arise in the context of programming language semantics and generalized metrization of non-Hausdorff topologies. Fuzzy equalities arise in the context of sheaves and fuzzy sets. It turns out that partial metrics and fuzzy equalities coincide.

More specifically, the axioms for partial metrics with values in quantales coincide modulo notation with the axioms given by U.Hoehle for Q-sets (M-valued sets, sets with fuzzy equality, quantale-valued sets) for the case of commutative quantales.

Omega-sets (sets valued in complete Heyting algebras) correspond to the case of partial ultrametrics.

Date received: May 4, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxs-40.