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
On the quasi-uniform convergence of transfinite sequences of functions.
On the Scott topology on the set of continuous maps
On topological groups with a small base and metrizability
A (Hausdorff) topological group is said to have a -base if it admits a base of neighbourhoods of the unit, , such that whenever β ≤ α for all . The class of all metrizable topological groups is a proper subclass of the class of all topological groups having a -base. We prove that a topological group is metrizable iff it is Fréchet-Urysohn and has a -base. We also show that any precompact set in a topological group is metrizable, and hence G is strictly angelic. We deduce from this result...
On topological properties of the spaces of Darboux Baire 1 functions and bounded derivatives
We investigate the topological structure of the space 𝓓ℬ₁ of bounded Darboux Baire 1 functions on [0,1] with the metric of uniform convergence and with the p*-topology. We also investigate some properties of the set Δ of bounded derivatives.
On transfinite convergence and generalized continuity
On transfinite sequences of mappings
Order intervals in . Compactness, coincidence of topologies, metrizability
Let be a compact space and let be the Banach lattice of real-valued continuous functions on . We establish eleven conditions equivalent to the strong compactness of the order interval in , including the following ones: (i) consists of isolated points of ; (ii) is pointwise compact; (iii) is weakly compact; (iv) the strong topology and that of pointwise convergence coincide on ; (v) the strong and weak topologies coincide on . Moreover, the weak topology and that of pointwise convergence...