New types of almost countable dense homogeneous space.
The definitions of AP and WAP were originated in categorical topology by A. Pultr and A. Tozzi, Equationally closed subframes and representation of quotient spaces, Cahiers Topologie Géom. Différentielle Catég. 34 (1993), no. 3, 167-183. In general, we have the implications: , where is defined as the property that every compact subset is closed and is defined as the property that every convergent sequence has at most one limit. And a space is called submaximal if every dense subset is open....
The structure of binary coproducts in the category of frames is analyzed, and the results are then applied widely in the study of compactness, local compactness (continuous frames), separatedness, pushouts and closed frame homomorphisms.
In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.