Teresa Abreu*

Eusébio Corbacho**

tabreu@ipca.pt

corbacho@uvigo.es

Abstract. In a non-empty set a filter on consisting of reflexive relations, which satisfies:

is called local quasi-uniformity. If we require the symmetry condition then we obtain a local uniformity. These concepts were introduced by Fletcher-Lindegren(1974) and Williams(1972) respectively.

We will discuss the possibility of extending the known results about (quasi)-uniform spaces to local (quasi)-uniform spaces.

Keywords: quasi-uniformity, local quasi-uniformity, local quasi-uniform space, quasi-uniform space, uniform space.

Texto completo disponível apenas em PDF.

Full text only available in PDF format.

Referências bibliográficas

Clifford A.H. and Preston G. B.(1961). The algebraic theory of semigroups. Mathematical Surveys I, 7, American Mathematical Society. Rhode Island .         [ Links ]

Császár, A.(1960). Fondements de la topologie génerale., Gauthier-Villars. Paris.

Dungundji, J.(1967). Topology. Ally and Bacon. Boston.

Fletcher, P.; Lindgren, W.(1974). Locally quasi-uniform spaces with countable bases. Duke Math. J,. 41, 231-340.

Fletcher, P.; Lindgren, W.(1982). Quasi-uniform spaces, Lecture Notes in Pure and Applied Mathematics. 77, Marcel Dekker, Inc.. New York.

Krishnan, V.S.(1955). A note on semiuniform spaces,. J. Madras, Univ. Sect. B, 25, 123-124.

Kelley, J.L (1975). General topology. Van Nostrand. Princeton.

Künzi, H.(1993). Quasi-Uniform spaces-eleven years later. Topology Proceedings, 18, 143–171.

Künzi, H.(2001). Nonsymmetric Distances and Their Associated Topologies: About the Origins of Basic Ideas in the Area of Asymetric Topology. Handbook of the history of general topology, 3, 853-968. Hist. Topol. 3, Kluwer Acad. Publ. Dordrecht.

Murdeshwar, M.G., Naimpally, S.A.(1966). Quasi-Uniform Topological Spaces. Noordhoff.

Nacbin, L.(1948 b). Sur les espaces uniformes ordonnés. C.R. Acad. Sci.Paris, 226, 774-775

Nacbin, L.(1965). Topology and Order. D. van Nostrand. Princeton.

Pervin,W.J. (1963). Quasi-uniformization of topological spaces. Math. Ann., 150, 316-317.

Picado, J. (1998) Weil Nearness Spaces, Portugaliae Mathematica, 55, (2) 233-254.

Williams, J.(1972). Loccally Uniform Spaces. Transactions of the American Mathematical Society, 168.

Weil, A. (1937). Sur les espaces à structure uniform et sur la topologie générale., Gauthier-Villars. Paris.

* ESG- Escola Superior de Gestão, Instituto Politécnico do Cávado e do Ave (IPCA)