The -topology and incompactness of
We establish a relation between covering properties (e.gĿindelöf degree) of two standard topological spaces (Lemmas 4 and 5). Some cardinal inequalities follow as easy corollaries.
The -topology on compact spaces
The Gruenhage property, property *, fragmentability, and σ-isolated networks in generalized ordered spaces
We examine the Gruenhage property, property * (introduced by Orihuela, Smith, and Troyanski), fragmentability, and the existence of σ-isolated networks in the context of linearly ordered topological spaces (LOTS), generalized ordered spaces (GO-spaces), and monotonically normal spaces. We show that any monotonically normal space with property * or with a σ-isolated network must be hereditarily paracompact, so that property * and the Gruenhage property are equivalent in monotonically normal spaces....
The Haar measure of certain sets in the Bohr group
The Hewitt realcompactification of a product (Preliminary communication)
The Hurewicz covering property and slaloms in the Baire space
According to a result of Kočinac and Scheepers, the Hurewicz covering property is equivalent to a somewhat simpler selection property: For each sequence of large open covers of the space one can choose finitely many elements from each cover to obtain a groupable cover of the space. We simplify the characterization further by omitting the need to consider sequences of covers: A set of reals X has the Hurewicz property if, and only if, each large open cover of X contains a groupable subcover. This...
The indexed open covering theorem
The injective hull and the bc-hull of a topological space.
The insertion of sets and fine topologies
The inverse image of a metric space under a biquotient compact mapping
The inverse images of hyperconnected sets
The -compactification of a topologized semigroup
The LCC-topology on the space of continuous functions
The Lindelöf number greater than continuum is u-invariant
2000 Mathematics Subject Classification: 54C35, 54D20, 54C60.Two Tychonoff spaces X and Y are said to be l-equivalent (u-equivalent) if Cp(X) and Cp(Y) are linearly (uniformly) homeomorphic. N. V. Velichko proved that countable Lindelöf number is preserved by the relation of l-equivalence. A. Bouziad strengthened this result and proved that any Lindelöf number is preserved by the relation of l-equivalence. In this paper it has been proved that the Lindelöf number greater than continuum is preserved...
The Lindelöf property and pseudo--compactness in spaces and topological groups
We introduce and study, following Z. Frol’ık, the class of regular -spaces such that the product is pseudo--compact, for every regular pseudo--compact -space . We show that every pseudo--compact space which is locally is in and that every regular Lindelöf -space belongs to . It is also proved that all pseudo--compact -groups are in . The problem of characterization of subgroups of -factorizable (equivalently, pseudo--compact) -groups is considered as well. We give some necessary...
The Lindelöf property in Banach spaces
A topological space (T,τ) is said to be fragmented by a metric d on T if each non-empty subset of T has non-empty relatively open subsets of arbitrarily small d-diameter. The basic theorem of the present paper is the following. Let (M,ϱ) be a metric space with ϱ bounded and let D be an arbitrary index set. Then for a compact subset K of the product space the following four conditions are equivalent: (i) K is fragmented by , where, for each S ⊂ D, . (ii) For each countable subset A of D, is...
The Lusin-Menchoff property of fine topologies
The Mal'tsev operation on countably compact spaces
The minimal ideals of a multiplicative and additive subsemigroup of ßN.