dc.contributor.author | Ozcag, Selma | |
dc.contributor.author | Brown, Lawrence A. | |
dc.date.accessioned | 2019-12-16T09:39:50Z | |
dc.date.available | 2019-12-16T09:39:50Z | |
dc.date.issued | 2006 | |
dc.identifier.issn | 0166-8641 | |
dc.identifier.uri | https://doi.org/10.1016/j.topol.2005.03.018 | |
dc.identifier.uri | http://hdl.handle.net/11655/19751 | |
dc.description.abstract | In this paper the authors consider the interplay between di-uniformities on a texture and a complementation on that texture. It is shown that with each di-uniformity corresponds a second di-uniformity, called its complement. Di-uniformities that coincide with their complement are then called complemented, and it is verified that the uniform ditopology of a complemented di-uniformity is a complemented ditopology. The connection with the uniform bicontinuity of the complement of a difunction is also considered. The relation between quasi-uniformities and uniformities on a set X in the classical sense is then investigated in the setting of di-uniformities on the complemented discrete texture on X. It is shown that di-uniformities on this discrete texture correspond in a one-to-one way with quasi-uniformities on X, a quasi-uniformity being a uniformity if and only if the corresponding di-uniforrnity is complemented. This shows that while the difference between quasi-uniformities and uniformities in the classical description is a question of symmetry, this becomes a matter of complementation in the di-uniform case. (C) 2006 Elsevier B.V. All rights reserved. | |
dc.language.iso | en | |
dc.publisher | Elsevier Science Bv | |
dc.relation.isversionof | 10.1016/j.topol.2005.03.018 | |
dc.rights | info:eu-repo/semantics/openAccess | |
dc.subject | Mathematics | |
dc.title | A Textural View of The Distinction Between Uniformities and Quasi-Uniformities | |
dc.type | info:eu-repo/semantics/article | |
dc.type | info:eu-repo/semantics/conferenceObject | |
dc.type | info:eu-repo/semantics/publishedVersion | |
dc.relation.journal | Topology And Its Applications | |
dc.contributor.department | Matematik | |
dc.identifier.volume | 153 | |
dc.identifier.issue | 17 | |
dc.identifier.startpage | 3294 | |
dc.identifier.endpage | 3307 | |
dc.description.index | WoS | |
dc.description.index | Scopus | |