A Method of Constructing Compatible Frame Quasi-uniformities

다국어 초록 (Multilingual Abstract)

Unlike a uniformity, a quasi-uniformity is not determined by its quasi-uniform covers. However, a classical construction, due to P. Fletcher, which assigns a transitive quasi-uniformity to each family of interior-preserving open covers, allows to describe all transitive quasi-uniformities on the topological spaces in terms of those families of covers. In this paper we develop a point free generalization of this, which solves a problem posed by G. C. L. Br¨ummer, together with various examples and applications that illustrateits remarkable usefulness. By this construction, many kinds of interior-preserving open covers (e.g. locally finite, point-finite, spectrum, well-monotone) induce compatible quasi-uniformities on an arbitrary frame.

참고문헌 (Reference)

1 "Weil Entourages in Pointfree Topology" universityof coimbra 1995

2 "The real numbers in pointfree topology" Universidade de Coimbra. 12 : 1997

3 "The cozero part of a biframe" 42 : 285-295, 2002

4 "Sublocale lattices" 168 : 309-326, 2002

5 "Structured Frames" university of cape town : 1987

6 "Strong zero-dimensionality of biframes andbispaces" 13 : 273-290, 1990

7 "Some problems in categorical and asymmetric topology" 2001

8 "Quasi-uniform spaces" new york : 1982

9 "Paracompact frames and closed maps" 16 : 93-116, 1975

10 "On totally bounded quasi-uniform spaces" 21 : 396-401, 1970

11 "On the paracompactness of frames" 33 : 485-491, 1992

12 "Functorial quasi-uniformities on frames" university of coimbra 2003

13 "Frames with transitive structures" 10 : 63-79, 2002

14 "Frame quasi-uniformities by entourages" University of Cape Town 161-175, 1999

15 "Biframe compactifications" 34 : 567-574, 1993

16 "A note on totally boundedness" 88 : 25-34, 2000