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Sequential Completeness for ⊤-Quasi-Uniform Spaces and a Fixed Point Theorem

Mathematics, 2022
We define sequential completeness for ⊤-quasi-uniform spaces using Cauchy pair ⊤-sequences. We show that completeness implies sequential completeness and that for ⊤-uniform spaces with countable ⊤-uniform bases, completeness and sequential completeness ...
Gunther Jäger
doaj   +4 more sources

The scale of a quasi-uniform space [PDF]

Acta Mathematica Hungarica, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Olivier Olela Otafudu
exaly   +3 more sources

Quasi-uniform Space

Formalized Mathematics, 2016
In this article, using mostly Pervin [9], Kunzi [6], [8], [7], Williams [11] and Bourbaki [3] works, we formalize in Mizar [2] the notions of quasiuniform space, semi-uniform space and locally uniform space.
Roland Coghetto
semanticscholar   +4 more sources

∗-half completeness in quasi-uniform spaces

Applied General Topology, 2009
Romaguera and Sánchez-Granero (2003) have introduced the notion of T1∗-half completion and used it to see when a quasi-uniform space has a ∗-compactification. In this paper, for any quasi-uniform space, we construct a ∗-half completion, called standard ∗-
Athanasios Andrikopoulos
doaj   +7 more sources

On quasi-uniform box products

Applied General Topology, 2017
We revisit the computation of entourage sections of the constant uniformity of the product of countably many copies the Alexandroff one-point compactification called the Fort space. Furthermore, we define the concept of a quasi-uniformity on a product of
Olivier Olela Otafudu, Hope Sabao
doaj   +2 more sources

Quasi-uniform convergence topologies on function spaces- Revisited

Applied General Topology, 2017
Let X and Y be topological space and F(X,Y) the set of all functions from X into Y. We study various quasi-uniform convergence topologies U_{A} (A⊆P(X)) on F(X,Y) and their comparison in the setting of Y a quasi-uniform space.
Wafa Khalaf Alqurash, Liaqat Ali Khan
doaj   +2 more sources

A Construction of the Pair Completion of a Quasi-Uniform Space [PDF]

Canadian Mathematical Bulletin, 1978
Although L. Nachbin introduced the concept of a quasiuniform space in connection with the study of uniform ordered spaces [7], it was A. Császár who first developed a theory of completion for these spaces. In the review of Császár′s work [3], J. Isbell wrote: “A topogenic space is already complete according to the present definition; an unfortunate ...
W. Lindgren, P. Fletcher
semanticscholar   +3 more sources

A COMPLETION FOR A QUASI UNIFORM SPACE [PDF]

Proceedings of the American Mathematical Society, 1967
R. Stoltenberg
semanticscholar   +3 more sources

Completeness in quasi-uniform spaces

Acta Mathematica Hungarica, 2004
The author defines and studies another kind of completeness for quasi-uniform spaces, based on Cauchy-pairs of nets. He constructs an accompanying completion and compares his definition with other notions of completeness and completions.
Athanasios Andrikopoulos
exaly   +3 more sources

A Note on Locally Quasi-Uniform Spaces

Canadian Mathematical Bulletin, 1976
AbstractLocally quasi-uniform spaces are studied, and it is shown that a topological space (X, t) admits exactly one compatible locally quasi-uniform structure if and only if t is finite.
T. Hicks, Shirley M. Huffman
semanticscholar   +3 more sources