The concept of a frame was introduced in the mid-sixties by Dowker and
Papert. Since then frames have been extensively studied by several authors,
including Banaschewski, Pultr and Baboolal to mention a few. The idea of a
nearness was first introduced by H. Herrlich in 1972 and that of a nearness
frame by Banaschewski in the late eighties. T. Dube made a fairly detailed
study of the latter concept.
The purpose of this thesis is to study the property of local finiteness and
metacompactness in the setting of nearness frames. J. W. Carlson studied
these ideas (including Lindelof and Pervin nearness structures) in the realm
of nearness spaces.
The first four chapters are a brief overview of frame theory culminating in
results concerning regular, completely regular, normal and compact frames.
In chapter five we provide the definitions for various nearness frames: Pervin,
Lindelof , Locally Finite and Metacompact to mention a few. A particular
locally finite nearness structure, denoted by µLF, is studied in detail. It
is defined to be the nearness structure on a regular frame L generated by
the family of all locally finite covers on the frame L. Also, a particular
metacompact nearness structure, denoted by µPF, is studied in detail. It is
defined to be the nearness structure on a regular frame L generated by the
family of all point-finite covers of the frame L. Various theorems related the
above nearness frames and these nearness structures are obtained. / Thesis (M.Sc.)-University of Durban-Westvile, 1998.
|Contributors||Baboolal, Deeva Lata., Ori, R. G.|
|Source Sets||South African National ETD Portal|
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