In:
Studia Scientiarum Mathematicarum Hungarica, Akademiai Kiado Zrt., Vol. 44, No. 3 ( 2007-09-1), p. 307-316
Abstract:
By a *-compactification of a T 0 quasi-uniform space ( X, U ) we mean a compact T 0 quasi-uniform space ( Y, V ) that has a T ( V ∨ V −1 )-dense subspace quasi-isomorphic to ( X, U ). We prove that ( X, U ) has a *-compactification if and only if its T 0 biocompletion \documentclass{aastex}
\usepackage{amsbsy} \usepackage{amsfonts}
\usepackage{amssymb} \usepackage{bm}
\usepackage{mathrsfs} \usepackage{pifont}
\usepackage{stmaryrd} \usepackage{textcomp}
\usepackage{upgreek} \usepackage{portland,xspace}
\usepackage{amsmath,amsxtra} \usepackage{bbm}
\pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6}
\begin{document} $$({\tilde X},\tilde {\mathcal{U}})$$
\end{document} is compact. We also show that, in this case, \documentclass{aastex}
\usepackage{amsbsy} \usepackage{amsfonts}
\usepackage{amssymb} \usepackage{bm}
\usepackage{mathrsfs} \usepackage{pifont}
\usepackage{stmaryrd} \usepackage{textcomp}
\usepackage{upgreek} \usepackage{portland,xspace}
\usepackage{amsmath,amsxtra} \usepackage{bbm}
\pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6}
\begin{document} $$({\tilde X},\tilde {\mathcal{U}})$$
\end{document} is the maximal *-compactification of ( X, U ) and ( X ∪ G ( X ), \documentclass{aastex}
\usepackage{amsbsy} \usepackage{amsfonts}
\usepackage{amssymb} \usepackage{bm}
\usepackage{mathrsfs} \usepackage{pifont}
\usepackage{stmaryrd} \usepackage{textcomp}
\usepackage{upgreek} \usepackage{portland,xspace}
\usepackage{amsmath,amsxtra} \usepackage{bbm}
\pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6}
\begin{document} $$\tilde {\mathcal{U}}$$
\end{document} | X ∪ G ( X ) ) is its minimal *-compactification, where G ( X ) is the set of all points of \documentclass{aastex}
\usepackage{amsbsy} \usepackage{amsfonts}
\usepackage{amssymb} \usepackage{bm}
\usepackage{mathrsfs} \usepackage{pifont}
\usepackage{stmaryrd} \usepackage{textcomp}
\usepackage{upgreek} \usepackage{portland,xspace}
\usepackage{amsmath,amsxtra} \usepackage{bbm}
\pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6}
\begin{document} $$\tilde X$$
\end{document} which are T ( \documentclass{aastex}
\usepackage{amsbsy} \usepackage{amsfonts}
\usepackage{amssymb} \usepackage{bm}
\usepackage{mathrsfs} \usepackage{pifont}
\usepackage{stmaryrd} \usepackage{textcomp}
\usepackage{upgreek} \usepackage{portland,xspace}
\usepackage{amsmath,amsxtra} \usepackage{bbm}
\pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6}
\begin{document} $$\tilde {\mathcal{U}}$$
\end{document} )-closed (we remark that as partial order of *-compactifications we use the inverse of the partial order used for T 2 compactifications of Tychonoff spaces). Applications of our results to some examples in theoretical computer science are given.
Type of Medium:
Online Resource
ISSN:
0081-6906
,
1588-2896
DOI:
10.1556/sscmath.2007.1022
Language:
Unknown
Publisher:
Akademiai Kiado Zrt.
Publication Date:
2007
SSG:
17,1
Permalink