Quasiorders on topological categories
| dc.creator | Trnkova, Vera | |
| dc.date | 2002-04-10 | |
| dc.date.accessioned | 2026-07-07T04:47:37Z | |
| dc.date.available | 2026-07-07T04:47:37Z | |
| dc.description | We prove that, for every cardinal number $α\geq {\mathfrak c}$, there exists a metrizable space $X$ with $|X|=α$ such that for every pair of quasiorders $\leq_1$, $\leq_2$ on a set $Q$ with $|Q| \leq α$ satisfying the implication $$q \leq_1 q' \implies q \leq_2 q'$$ there exists a system $\{X(q) : q\in Q\}$ of non-homeomorphic clopen subsets of $X$ with the following properties: (1) $q \leq_1 q'$ if and only if $X(q)$ is homeomorphic to a clopen subset of $X(q')$, (2) $q \leq_2 q'$ implies that $X(q)$ is homeomorphic to a closed subset of $X(q')$ and (3) $\neg (q \leq_2 q')$ implies that there is no one-to-one continuous map of $X(q)$ into $X(q')$. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0204143 | |
| dc.identifier | http://arxiv.org/abs/math/0204143 | |
| dc.identifier | Proceedings of the Ninth Prague Topological Symposium, (Prague, 2001), pp. 321--330, Topology Atlas, Toronto, 2002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63786 | |
| dc.subject | General Topology | |
| dc.subject | 54B30, 54H10 | |
| dc.title | Quasiorders on topological categories | |
| dc.type | text |