Results 1 to 10 of about 125 (64)

Smyth completion as bicompletion [PDF]

Topology and Its Applications, 1999
In his thesis \textit{H. J. K. Junnila} defined the well-monotone quasi-uniformity \({\mathcal W}(X) \) of a topological space \(X\). \textit{N. Ferrario} and \textit{H. P. A. Künzi} [Math. Proc. Camb. Philos. Soc. 109, No. 1, 167-186 (1991; Zbl 0731.54021)] then showed that the sobrification of a \(T_0\)-space \(X\) can be constructed as the ...
Ralph Kopperman
exaly   +5 more sources

The bicompletion of fuzzy quasi-metric spaces [PDF]

Fuzzy Sets and Systems, 2011
Extending the well-known result that every fuzzy metric space, in the sense of Kramosil and Michalek, has a completion which is unique up to isometry, we show that every KM-fuzzy quasi-metric space has a bicompletion which is unique up to isometry, and deduce that for each KM-fuzzy quasi-metric space, the completion of its induced fuzzy metric space ...
S Romaguera
exaly   +6 more sources

Ordered compactifications and families of maps

International Journal of Mathematics and Mathematical Sciences, 1997
For a T3.5-ordered space, certain families of maps are designated as “defining families.“ For each such defining family we construct the smallest T2-ordered compactification such that each member of the family can be extended to the compactification ...
D. M. Liu, D. C. Kent
doaj   +3 more sources

Symmetry Conditions on the Coincidence of Some Notions of Quasi-Uniform Completeness [PDF]

International Journal of Mathematics and Mathematical Sciences, 2007
We generalize the notions of quietness and semisymmetry defined by Doitchinov (1991) and Deák (1991) and we study the role of these extended notions on the coincidence of some well-known quasi-uniform completeness.
Athanasios Andrikopoulos
doaj   +3 more sources

Asymmetry and bicompletion of approach spaces [PDF]

Topology and Its Applications, 2006
The authors introduce a functor of symmetrizing approach spaces and then develop a bicompletion theory for \(T_0\) approach spaces, which extends the the completion theory of Hausdorff uniform approach spaces obtained by \textit{R. Lowen} and \textit{K. Robeys} [ Q. J. Math., Oxf. II. Ser. 43, No. 171, 319--338 (1992; Zbl 0796.54033)].
M Sioen
exaly   +5 more sources

The bicompletion of the Hausdorff quasi-uniformity [PDF]

Topology and Its Applications, 2009
We study conditions under which the Hausdorff quasi-uniformity ${\mathcal U}_H$ of a quasi-uniform space $(X,{\mathcal U})$ on the set ${\mathcal P}_0(X)$ of the nonempty subsets of $X$ is bicomplete. Indeed we present an explicit method to construct the bicompletion of the $T_0$-quotient of the Hausdorff quasi-uniformity of a quasi-uniform space.
Hans-Peter A Kunzi, S Romaguera
exaly   +5 more sources

More on upper bicompletion-true functorial quasi-uniformities [PDF]

Topology and Its Applications, 2011
Let \({\mathbf Q}{\mathbf U}_0\) be the category of quasi-uniform \(T_0\)-spaces and \(K:{\mathbf Q}{\mathbf U}_0\to{\mathbf Q}{\mathbf U}_0\) be the bicompletion reflector. If \(T:{\mathbf Q}{\mathbf U}_0\to{\mathbf T}{\mathbf o}{\mathbf p}_0\) is the forgetful functor to the category \({\mathbf T}{\mathbf o}{\mathbf p}_0\) of topological \(T_0 ...
Hans-Peter A Kunzi
exaly   +5 more sources

Functorial approach structures [PDF]

Applied General Topology, 2003
We show that there exists at least a proper class of functorial approach structures, i.e., right inverses to the forgetful functor T : AP→ Top (where AP denotes the topological construct of approach spaces and contractions as introduced by R.
Guillaume C.L. Brümmer, Mark Sioen
doaj   +2 more sources

The congruence biframe as a quasi-uniform bicompletion [PDF]

Topology and Its Applications, 2020
Künzi and Ferrario have shown that a $T_0$ space is sober if and only if it is bicomplete in the well-monotone quasi-uniformity. We prove a pointfree version of this result: a strictly zero-dimensional biframe is a congruence biframe if and only if it is bicomplete in the same quasi-uniformity.
Graham Manuell
exaly   +4 more sources

On bicomplete quasi-pseudometrizability

Topology and its Applications, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Romaguera, Salvador, Salbany, Sergio
openaire   +6 more sources