Quasi-uniform structures determined by closure operators
| dc.contributor.author | Holgate, D | |
| dc.contributor.author | Iragi, M | |
| dc.date.accessioned | 2021-04-15T09:17:51Z | |
| dc.date.available | 2021-04-15T09:17:51Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | We demonstrate a one-to-one correspondence between idempotent closure operators and the so-called saturated quasi-uniform structures on a category C. Not only this result allows to obtain a categorical counterpart P of the Császár-Pervin quasi-uniformity P, that we characterize as a transitive quasi-uniformity compatible with an idempotent interior operator, but also permits to describe those topogenous orders that are induced by a transitive quasi-uniformity on C. The categorical counterpart P⁎ of P−1 is characterized as a transitive quasi-uniformity compatible with an idempotent closure operator. When applied to other categories outside topology P allows, among other things, to generate a family of idempotent closure operators on Grp, the category of groups and group homomorphisms, determined by the normal closure. | en_US |
| dc.identifier.citation | Holgate, D., & Iragi, M. (2021). Quasi-uniform structures determined by closure operators. Topology and its Applications, 295,107669 | en_US |
| dc.identifier.issn | 0166-8641 | |
| dc.identifier.uri | 10.1016/j.topol.2021.107669 | |
| dc.identifier.uri | http://hdl.handle.net/10566/6042 | |
| dc.language.iso | en | en_US |
| dc.publisher | Elsevier | en_US |
| dc.subject | Closure operator | en_US |
| dc.subject | Quasi-uniform structure | en_US |
| dc.subject | Syntopogenous structure | en_US |
| dc.subject | Topogenous orders | en_US |
| dc.subject | Homomorphisms | en_US |
| dc.title | Quasi-uniform structures determined by closure operators | en_US |
| dc.type | Article | en_US |