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Quasi-uniform completions of partially ordered spaces

In: Mathematica Slovaca, vol. 57, no. 2
David Buhagiar - Tanja Telenta
Detaily:
Rok, strany: 2007, 189 - 200
O článku:
In this paper we define partially ordered quasi-uniform spaces $(X,\mathfrak{U},≤)$ (PO-quasi-uniform spaces) as those spaces with a biconvex quasi-uni formity $\mathfrak{U}$ on the poset $(X,≤)$ and give a construction of a (transitive) biconvex compatible quasi-uniformity on a partially ordered topological space when its topology satisfies certain natural conditions. We also show that under certain conditions on the topology $τ_{\mathfrak{U}*}$ of a PO-quasi-uniform space $(X,\mathfrak{U},≤)$, the bicompletion $(\widetilde{X},\widetilde{\mathfrak{U}})$ of $(X,\mathfrak{U})$ is also a PO-quasi-uniform space $(\widetilde{X},\widetilde{\mathfrak{U}},\preceq)$ with a partial order $\preceq$ on $\widetilde{X}$ that extends $≤$ in a natural way.
Ako citovať:
ISO 690:
Buhagiar, D., Telenta, T. 2007. Quasi-uniform completions of partially ordered spaces. In Mathematica Slovaca, vol. 57, no.2, pp. 189-200. 0139-9918.

APA:
Buhagiar, D., Telenta, T. (2007). Quasi-uniform completions of partially ordered spaces. Mathematica Slovaca, 57(2), 189-200. 0139-9918.