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.
In this article we introduce the notion of strongly -spaces, that is, those spaces in which countably compact subsets are closed. We find they have good properties. We prove that a space is maximal countably compact if and only if it is minimal strongly , and apply this result to study some properties of minimal strongly -spaces, some of which are not possessed by minimal -spaces. We also give a positive answer to a question proposed by O. T. Alas and R. G. Wilson, who asked whether every...
An -space is a topological space in which the topology is generated by the family of all -sets (see [N]). In this paper, minimal--spaces (where denotes several separation axioms) are investigated. Some new characterizations of -spaces are also obtained.
A space is monotonically Lindelöf (mL) if one can assign to every open cover a countable open refinement so that refines whenever refines . We show that some countable spaces are not mL, and that, assuming CH, there are countable mL spaces that are not second countable.
Some results concerning spaces with countably weakly uniform bases are generalized for spaces with -in-countable ones.
is non-normal for any metrizable crowded space and an arbitrary point .
Let a space be Tychonoff product of -many Tychonoff nonsingle point spaces . Let Suslin number of be strictly less than the cofinality of . Then we show that every point of remainder is a non-normality point of its Čech–Stone compactification . In particular, this is true if is either or and a cardinal is infinite and not countably cofinal.
The minimum weight of a nowhere first-countable compact space of countable -weight is shown to be , the least cardinal for which the real line can be covered by many nowhere dense sets.