On sequence-covering --images of locally separable metric spaces
On sequential convergence in weakly compact subsets of Banach spaces
We construct an example of a Banach space E such that every weakly compact subset of E is bisequential and E contains a weakly compact subset which cannot be embedded in a Hilbert space equipped with the weak topology. This answers a question of Nyikos.
On sets of confluent and related mappings in the space
On sets of points of semicontinuity in fine topologies generated by an ideal
On shape
On shape and fundamental deformation retracts
On shape and fundamental deformation retracts II
On shape groups and Cech homology groups of a compact space
On shape of hyperspaces
On simultaneous Blumberg sets
On Simultaneous Fixed Points of Multi-Valued Maps.
On singlevaluedness and (strong) upper semicontinuity of maximal monotone mappings
On single-valuedness of set-valued maps satisfying linear inclusions.
On small systems and compact families of Borel functions
On smooth continua
On some applications of infinite-dimensional manifolds to the theory of shape
On some classes of compact spaces lying in -products
On some conditions which imply the continuity of almost all sections
Let be an open interval, a topological space and a metric space. Some local conditions implying continuity and quasicontinuity of almost all sections of a function are shown.
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 generalizations of the Kakutani-Stone and Stone-Weierstrass theorems.
For a completely regular space X, C*(X) denotes the algebra of all bounded real-valued continuous functions over X. We consider the topology of uniform convergence over C*(X).When K is a compact space, the Stone-Weierstrass and Kakutani-Stone theorems provide necessary and sufficient conditions under which a function f ∈ C*(K) can be uniformly approximated by members of an algebra, lattice or vector lattice of C*(K). In this way, the uniform closure and, in particular, the uniform density of algebras...