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Samuel compactification and uniform coreflection of nearness σ -frames

Inderasan Naidoo — 2006

Czechoslovak Mathematical Journal

We introduce the structure of a nearness on a σ -frame and construct the coreflection of the category 𝐍 σ F r m of nearness σ -frames to the category 𝐊 R e g σ F r m of compact regular σ -frames. This description of the Samuel compactification of a nearness σ -frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform σ -frames in [11]. We also construct the uniform coreflection of a nearness σ -frame, that is, the coreflection of the category of 𝐍 σ F r m to the category...

A study of universal elements in classes of bases of topological spaces

Dimitris N. Georgiou;  Athanasios C. Megaritis;  Inderasan Naidoo;  Fotini Sereti — 2021

Commentationes Mathematicae Universitatis Carolinae

The universality problem focuses on finding universal spaces in classes of topological spaces. Moreover, in “Universal spaces and mappings” by S. D. Iliadis (2005), an important method of constructing such universal elements in classes of spaces is introduced and explained in details. Simultaneously, in “A topological dimension greater than or equal to the classical covering dimension” by D. N. Georgiou, A. C. Megaritis and F. Sereti (2017), new topological dimension is introduced and studied, which...

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