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Nonstandard methods of completing quasi-uniform spaces

Topology and Its Applications, 1995
A rather general method of constructing T2-completions of a quasi-uniform space is given. Using it we show that a sufficient condition for a quasi-uniform space to have a T2-completion is that the quasi-uniformity contains a compatible uniformity.
Hermann Render
exaly   +2 more sources

A concept of completeness of quasi-uniform spaces

Topology and Its Applications, 1991
We define a notion of completion for quasi-uniform spaces in a categorical manner, and construct such completions for a large class of spaces (called quiet quasi-uniform spaces).
Doitchinov, Doitchin
exaly   +2 more sources

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Boundedness in a Quasi-Uniform Space

Canadian Mathematical Bulletin, 1970
Although a nontopological concept, boundedness seems to be of considerable importance in a topological space. 'There are many topological problems in which it is essential to be able to make this distinction' (between bounded and unbounded sets) [1].
Murdeshwar, M. G., Theckedath, K. K.
openaire   +2 more sources

Separation and Epimorphisms in Quasi-Uniform Spaces

Applied Categorical Structures, 2000
It is well known that the category of uniform spaces allows only for relatively few closure operators in the categorical sense. In contrast to this, the present paper shows that the category \textbf{QUnif} of quasi-uniform spaces carries plenty of different closure operators which then are studied comprehensively.
Dikran Dikranjan, Hans-Peter A. Künzi
openaire   +2 more sources

Some Results on Quasi-Uniform Spaces

Canadian Mathematical Bulletin, 1976
Constructions are made of a T1 space which does not have a T1 completion and of a quasi-uniform space which is complete, but not strongly complete. An example relating to a completion due to Popa is given. An alternate definition for Cauchy filter, called C-filter, is examined and a construction of a C-completion is given.
Carter, Karen S., Hicks, T. L.
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FIBREWISE BICOMPLETE QUASI-UNIFORM SPACES

Far East Journal of Mathematical Sciences (FJMS), 2015
Summary: We introduce the notion of complete quasi-uniform spaces over a base space \(B\) and give some properties of these spaces. We introduce a general method to obtain fibrewise completion of quasi-uniform spaces over \(B\) and give internal descriptions of fibrewise completions for two different types.
Park, Jin Won, Lee, Byung Sik
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On Optimization Problems in Quasi-uniform Spaces

Third International Conference on Natural Computation (ICNC 2007), 2007
This paper is concerned with optimization problems in T0 quasi-uniform spaces. Many optimization problems such as vector optimization, set-valued optimization, are unified in the quasi-uniform space to have a simple expression. Firstly, the proposition that a quasi-uniform space is T0 if and only if the intersection of all entourages of the quasi ...
Shao-ai Chen, Wen Li, Du Zou, Shaobai Chen   +3 more
openaire   +1 more source

Completeness in probabilistic quasi-uniform spaces

Fuzzy Sets and Systems, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yueli Yue, Jinming Fang
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Stability in quasi-uniform spaces and the inverse problem

Topology and Its Applications, 1993
We study the concept of a stable quasi-uniform space due to D. Doitchivov. In particular quasi-pseudo-metric spaces (X,d) whose associated quasi-uniformities U(d) or U(d-1) are stable are ...
Hans-Peter A Kunzi, Heikki J K Junnila
exaly   +2 more sources

Cowellpoweredness of Some Categories of Quasi-Uniform Spaces

Applied Categorical Structures, 2018
It is known that there is no example of a subcategory of the category $\mathbf{Unif}$ of uniform spaces that is non-cowellpowered. This paper is concerned with cowellpoweredness of subcategories of $\mathbf{QUnif}$, the category of quasi-uniform spaces, and shows that it has is a lot of cowellpowered and non-cowellpowered subcategories.
Dikran Dikranjan, Hans-Peter A. Künzi
openaire   +1 more source