Uniformities and covering properties for partial frames (II)

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Abstract


Abstract. This paper is a continuation of [2], in which we make use of
the notion of a partial frame, which is a meet-semilattice in which certain
designated subsets are required to have joins, and nite meets distribute over
these. After presenting there our axiomatization of partial frames, which we
call S-frames, we added structure, in the form of S-covers and nearness.
Here, in the unstructured setting, we consider regularity, normality and
compactness, expressing all these properties in terms of S-covers. We see
that an S-frame is normal and regular if and only if the collection of all nite
S-covers forms a basis for an S-uniformity on it. Various results about strong
inclusions culminate in the proposition that every compact, regular S-frame
has a unique compatible S-uniformity.

Keywords


Frame, S-frame, Z-frame, partial frame, -frame, -frame, meet-semilattice, near- ness, uniformity, strong inclusion, uniform map, core ection, P-approximation, strong, totally bounded, regular, normal, compact. Mathematics Subject Classication [2010]: 0

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References


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