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T 2 and T 3 objects at p in the category of proximity spaces

Muammer Kula, Samed Özkan (2020)

Mathematica Bohemica

In previous papers, various notions of pre-Hausdorff, Hausdorff and regular objects at a point p in a topological category were introduced and compared. The main objective of this paper is to characterize each of these notions of pre-Hausdorff, Hausdorff and regular objects locally in the category of proximity spaces. Furthermore, the relationships that arise among the various Pre T 2 , T i , i = 0 , 1 , 2 , 3 , structures at a point p are investigated. Finally, we examine the relationships between the generalized separation...

The category of compactifications and its coreflections

Anthony W. Hager, Brian Wynne (2022)

Commentationes Mathematicae Universitatis Carolinae

We define “the category of compactifications”, which is denoted CM, and consider its family of coreflections, denoted corCM. We show that corCM is a complete lattice with bottom the identity and top an interpretation of the Čech–Stone β . A c ∈ corCM implies the assignment to each locally compact, noncompact Y a compactification minimum for membership in the “object-range” of c . We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate the atoms...

The category of uniform spaces as a completion of the category of metric spaces

Jiří Adámek, Jan Reiterman (1992)

Commentationes Mathematicae Universitatis Carolinae

A criterion for the existence of an initial completion of a concrete category 𝐊 universal w.r.tḟinite products and subobjects is presented. For 𝐊 = metric spaces and uniformly continuous maps this completion is the category of uniform spaces.

The notion of closedness in topological categories

Mehmet Baran (1993)

Commentationes Mathematicae Universitatis Carolinae

In [1], various generalizations of the separation properties, the notion of closed and strongly closed points and subobjects of an object in an arbitrary topological category are given. In this paper, the relationship between various generalized separation properties as well as relationship between our separation properties and the known ones ([4], [5], [7], [9], [10], [14], [16]) are determined. Furthermore, the relationships between the notion of closedness and strongly closedness are investigated...

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