Summer Conference on Topology and Its Applications

Document Type

Topology + Asymmetric Structures

Publication Date


Publication Source

32nd Summer Conference on Topology and Its Applications


Mathematically modeling the question of how to satisfactorily compare, in many-valued ways, both bitstrings and the predicates which they might satisfy-a surprisingly intricate question when the conjunction of predicates need not be commutative-applies notions of enriched categories and enriched functors. Particularly relevant is the notion of a set enriched by a po-groupoid, which turns out to be a many-valued preordered set, along with enriched functors extended as to be "variable-basis". This positions us to model the above question by constructing the notion of topological systems enriched by many-valued preorders, systems whose associated extent spaces motivate the notion of topological spaces enriched by many-valued preorders, spaces which are non-commutative when the underlying lattice-theoretic base is equipped with a non-commutative (semi-)tensor product. Of special interest are crisp and many-valued specialization preorders generated by many-valued topological spaces, orders having these consequences for many-valued spaces: they characterize the well-established L-T0 separation axiom, define the L-T1(1) separation axiom-logically equivalent under appropriate lattice-theoretic conditions to the L-T1 axiom of T. Kubiak, and define an apparently new L-T1(2) separation axiom. Along with the consequences of such ideas for many-valued spectra, these orders show that asymmetry has a home in many-valued topology comparable in at least some respects to its home in traditional topology.


This document is available for download with the permission of the presenting author and the organizers of the conference. Permission documentation is on file.

Technological limitations may prevent some mathematical symbols and functions from displaying correctly in this record’s metadata fields. Please refer to the attached PDF for the correct display.