On small systems and compact families of Borel functions
On some classes of compact spaces lying in -products
On some fan-tightness type properties
Properties similar to countable fan-tightness are introduced and compared to countable tightness and countable fan-tightness. These properties are also investigated with respect to function spaces and certain classes of continuous mappings.
On some properties of the spaces of almost continuous functions.
On supertightness and function spaces
On Surjective Bing Maps
In [7], M. Levin proved that the set of all Bing maps of a compact metric space to the unit interval is a dense -subset of the space of all maps. In [6], J. Krasinkiewicz independently proved that the set of all Bing maps of a compact metric space to an n-dimensional manifold (n ≥ 1) is a dense -subset of the space of maps. In [9], J. Song and E. D. Tymchatyn, solving some problems of J. Krasinkiewicz ([6]), proved that the set of all Bing maps of a compact metric space to a nondegenerate connected...
On the Banach-Stone Theorem.
On the cardinality of Lindelöf subspaces of function spaces
On the completeness of a topological group of functions.
On the connected-open topology
On the Connes operator in Hochschild homology.
On the extent of star countable spaces
For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have...
On the Fréchet-Urysohn property in spaces of continuous functions
On the functor of order-preserving functionals
We introduce a functor of order-preserving functionals which contains some known functors as subfunctors. It is shown that this functor is weakly normal and generates a monad.
On the homotopy equivalence of the spaces of proper and local maps
We prove that for n > 1 the space of proper maps P 0(n, k) and the space of local maps F 0(n, k) are not homotopy equivalent.
On the l-equivalence of metric spaces
On the Lindelöf property of spaces of continuous functions over a Tychonoff space and its subspaces
We study relations between the Lindelöf property in the spaces of continuous functions with the topology of pointwise convergence over a Tychonoff space and over its subspaces. We prove, in particular, the following: a) if is Lindelöf, , and the point has countable character in , then is Lindelöf; b) if is a cozero subspace of a Tychonoff space , then and .
On the position of the set of monotone mappings in function spaces
On the problem of preserving the class of continuous real functions
On the Productivity of l_1(Γ) Embeddings