Some notes on connectedness in nearness frames

Abstract

We study the uniform connection properties of uniform local connectedness, a weaker variant of the latter, and a certain property S in the context of nearness frames. We show that the uniformly locally connected nearness frames form a reflective subcategory of the category of nearness frames whose underlying frame is locally connected. Amongst other results we show that these uniform connection properties are conserved and reflected by perfect nearness extensions which are uniformly regular.

Mathematics Subject Classification (2010): Primary 06D22; Secondary 16D90, 54E17,
54D05.

Key words: Nearness frame, uniform connectedness, uniform local connectedness, property
S, reflective subcategory, uniformly regular nearness frame.