We introduce a new kind of cover called a normal isolator cover to characterize maximal Tychonoff spaces. Such a study is used to provide an alternative proof of an interesting result of Feng and Garcia-Ferreira in 1999 that every maximal Tychonoff space is extremally disconnected. Maximal tychonoffness of subspaces is also discussed.

Stalnaker introduced a combined epistemic-doxastic logic that can formally express a strong concept of belief, a concept which captures the ‘epistemic possibility of knowledge’. In this paper we first provide the most general extensional semantics for this concept of ‘strong belief’, which validates the principles of Stalnaker’s epistemic-doxastic logic. We show that this general extensional se...

Eric van Douwen [vD93] produced a maximal crowded extremally disconnected regular space and showed that its Stone-Čech compactification is an at most two-to-one image of βN. We prove that there are non-homeomorphic such images. We also develop some related properties of spaces which are absolute retracts of βN expanding on earlier of work in [BBS94, Sim87].

It will be convenient to call a space X a ParoviZenko space if (cy) X is a zero-dimensional compact space without isolated points, (p) every two disjoint open F,-sets have disjoint closures, and (y) every nonempty GG-set in X has non-empty interior. Compact spaces satisfying (p) are usually called F-spaces, while spaces satisfying (y) are called almost-P spaces. Examples of F-spaces are the ext...

Eric van Douwen [5] produced a maximal crowded extremally disconnected regular space and showed that its Čech–Stone compactification is an at most two-to-one image of βN. We construct for any n = 3 an example of a compact crowded space Xn that is an image of βN under a map all of whose fibers have either size n or n− 1. We also show that under CH this is best possible.

This paper deals with extremally disconnected spaces and P-spaces. A space X is said to be if, for every open subset V of X, the closure in also an set. P-spaces are which intersection countably many sets The authors present a new characterization spaces, P-spaces, by means selection theory. If either or P-space, then usual theorems extension real-valued continuous functions dense S can deduced...