Measure theoretic behavior of closed sets
Measure-theoretic characterizations of hereditarily-normal spaces.
New characterizations of regular open sets, semi-regular sets, and extremally disconnectedness
Non-accessible points in extremally disconnected compact spaces I
Numerical invariants of 0-dimensional spaces and their Cartesian multiplication.
On absolute retracts of ω*
An extremally disconnected space is called an absolute retract in the class of all extremally disconnected spaces if it is a retract of any extremally disconnected compact space in which it can be embedded. The Gleason spaces over dyadic spaces have this property. The main result of this paper says that if a space X of π-weight is an absolute retract in the class of all extremally disconnected compact spaces and X is homogeneous with respect to π-weight (i.e. all non-empty open sets have the same...
On covering properties by regular closed sets.
On fuzzy -compact spaces and fuzzy -extremally disconnected spaces
On generalizations of regular-Lindelöf spaces.
On inhomogeneity of products of compact F-spaces
On projectiveness in H-closed spaces
On spaces whose nowhere dense subsets are scattered.
On strongly precontinuous functions.
On the existence of P-points in the Stone-Čech compactification of integers
On the existence of true uniform ultrafilters
We shall show that there is an ultrafilter on singular with countable cofinality, which cannot be reached from the set of all subuniform ultrafilters by iterating the closure of sets of size .
On topological and algebraic structure of extremally disconnected semitopological groups
Starting with a very simple proof of Frol’ık’s theorem on homeomorphisms of extremally disconnected spaces, we show how this theorem implies a well known result of Malychin: that every extremally disconnected topological group contains an open and closed subgroup, consisting of elements of order . We also apply Frol’ık’s theorem to obtain some further theorems on the structure of extremally disconnected topological groups and of semitopological groups with continuous inverse. In particular, every...
Open mappings on extremally disconnected compact spaces
-sets and skeletal mappings
We prove that if the topology on the set Seq of all finite sequences of natural numbers is determined by -filters and λ ≤ , then Seq is a -set in its Čech-Stone compactification. This improves some results of Simon and of Juhász and Szymański. As a corollary we obtain a generalization of a result of Burke concerning skeletal maps and we partially answer a question of his.
Pasting topological spaces at one point
Let be a family of topological spaces and , for every . Suppose is the quotient space of the disjoint union of ’s by identifying ’s as one point . We try to characterize ideals of according to the same ideals of ’s. In addition we generalize the concept of rank of a point, see [9], and then answer the following two algebraic questions. Let be an infinite cardinal. (1) Is there any ring and an ideal in such that is an irreducible intersection of prime ideals? (2) Is there...
P-ideals and F-ideals in rings of continuous functions