Cell-like resolutions preserving cohomological dimensions.
We study relations between the cellularity and index of narrowness in topological groups and their -modifications. We show, in particular, that the inequalities and hold for every topological group and every cardinal , where denotes the underlying group endowed with the -modification of the original topology of and is the index of narrowness of the group . Also, we find some bounds for the complexity of continuous real-valued functions on an arbitrary -narrow group understood...
Given a discrete group , we consider the set of all subgroups of endowed with topology of pointwise convergence arising from the standard embedding of into the Cantor cube . We show that the cellularity for every abelian group , and, for every infinite cardinal , we construct a group with .
The aim this paper is to present an answer to Problem 1 of Monk [10], [11]. We do this by proving in particular that if μ is a strong limit singular cardinal, and then there are Boolean algebras such that . Further we improve this result, deal with the method and the necessity of the assumptions. In particular we prove that if is a ccc Boolean algebra and then satisfies the λ-Knaster condition (using the “revised GCH theorem”).
We discuss various generalizations of the class of Lindelöf spaces and study the difference between two of these generalizations, the classes of star-Lindelöf and centered-Lindelöf spaces.
A bottleneck in a dendroid is a continuum that intersects every arc connecting two non-empty open sets. Piotr Minc proved that every dendroid contains a point, which we call a center, contained in arbitrarily small bottlenecks. We study the effect that the set of centers in a dendroid has on its structure. We find that the set of centers is arc connected, that a dendroid with only one center has uncountably many arc components in the complement of the center, and that, in this case, every open set...
A subset of a metric space is central iff for every Katětov map upper bounded by the diameter of and any finite subset of there is such that for each . Central subsets of the Urysohn universal space (see introduction) are studied. It is proved that a metric space is isometrically embeddable into as a central set iff has the collinearity property. The Katětov maps of the real line are characterized.