Nonisomorphic thin-tall superatomic Boolean algebras
Non-normality and relative normality of Niemytzki plane
Non-normality points and nice spaces
J. Terasawa in " are non-normal for non-discrete spaces " (2007) and the author in “On non-normality points and metrizable crowded spaces” (2007), independently showed for any metrizable crowded space that each point of its Čech–Stone remainder is a non-normality point of . We introduce a new class of spaces, named nice spaces, which contains both of Sorgenfrey line and every metrizable crowded space. We obtain the result above for every nice space.
Nonsupercompactness and the reduced measure algebra
Normal P-spaces and the -topology
Not all dyadic spaces are supercompact
Null sequences cellular decompositions of
Numerical invariants of 0-dimensional spaces and their Cartesian multiplication.
On a class of almost discrete, abstract
On a construction of perfectly normal spaces and its applications to dimension theory
On a Corson space of Todorčević
On -Kasch spaces
If is a Tychonoff space, its ring of real-valued continuous functions. In this paper, we study non-essential ideals in . Let be a infinite cardinal, then is called -Kasch (resp. -Kasch) space if given any ideal (resp. -ideal) with then is a non-essential ideal. We show that is an -Kasch space if and only if is an almost -space and is an -Kasch space if and only if is a pseudocompact and almost -space. Let denote the socle of . For a topological space with only...
On a problem of Nogura about the product of Fréchet-Urysohn -spaces
Assuming Martin’s Axiom, we provide an example of two Fréchet-Urysohn -spaces, whose product is a non-Fréchet-Urysohn -space. This gives a consistent negative answer to a question raised by T. Nogura.
On a simply connected 1-dimensional continuum without the fixed point property
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 butterfly-points in , Tychonoff products and weak Lindelöf numbers
Let be the Tychonoff product of -many Tychonoff non-single point spaces . Let be a point in the closure of some whose weak Lindelöf number is strictly less than the cofinality of . Then we show that is not normal. Under some additional assumptions, is a butterfly-point in . In particular, this is true if either or and is infinite and not countably cofinal.
On certain separable and connected refinements of the Euclidean topology
On character and chain conditions in images of products
A scadic space is a Hausdorff continuous image of a product of compact scattered spaces. We complete a theorem begun by G. Chertanov that will establish that for each scadic space X, χ(X) = w(X). A ξ-adic space is a Hausdorff continuous image of a product of compact ordinal spaces. We introduce an either-or chain condition called Property which we show is satisfied by all ξ-adic spaces. Whereas Property is productive, we show that a weaker (but more natural) Property is not productive. Polyadic...
On co-lc topologies
On compactness and finiteness in topological spaces