Uniform type structures

 

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:

∀ χ ε Χ ∀ Q, ∃ P ε Q such that P ° P [χ] ⊂ Q [χ]

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.

 

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

** UV – Universidade de Vigo