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𝒯 0 - and 𝒯 1 -reflections

Maria Manuel Clementino (1992)

Commentationes Mathematicae Universitatis Carolinae

In an abstract category with suitable notions of subobject, closure and point, we discuss the separation axioms T 0 and T 1 . Each of the arising subcategories is reflective. We give an iterative construction of the reflectors and present characteristic examples.

A short note on separable frames

Themba Dube (1996)

Commentationes Mathematicae Universitatis Carolinae

Following the introduction of separability in frames ([2]) we investigate further properties of this notion and establish some consequences of the Urysohn metrization theorem for frames that are frame counterparts of corresponding results in spaces. In particular we also show that regular subframes of compact metrizable frames are metrizable.

Axiom T D and the Simmons sublocale theorem

Jorge Picado, Aleš Pultr (2019)

Commentationes Mathematicae Universitatis Carolinae

More precisely, we are analyzing some of H. Simmons, S. B. Niefield and K. I. Rosenthal results concerning sublocales induced by subspaces. H. Simmons was concerned with the question when the coframe of sublocales is Boolean; he recognized the role of the axiom T D for the relation of certain degrees of scatteredness but did not emphasize its role in the relation between sublocales and subspaces. S. B. Niefield and K. I. Rosenthal just mention this axiom in a remark about Simmons’ result. In this...

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