On relations approximated by continuous functions
On relative -starLindelöfness.
On relatively almost countably compact subsets
A subset of a space is almost countably compact in if for every countable cover of by open subsets of , there exists a finite subfamily of such that . In this paper we investigate the relationship between almost countably compact spaces and relatively almost countably compact subsets, and also study various properties of relatively almost countably compact subsets.
On relatively almost Lindelöf subsets
A subspace of a space is almost Lindelöf (strongly almost Lindelöf) in if for every open cover of (of by open subsets of ), there exists a countable subset of such that . In this paper we investigate the relationships between relatively almost Lindelöf subset and relatively strongly almost Lindelöf subset by giving some examples, and also study various properties of relatively almost Lindelöf subsets and relatively strongly almost Lindelöf subsets.
On relatively contractive relations in pairs of generalized uniform spaces.
J. C. Mathews and D. W. Curtis, [4], have introduced some structures which generalize structures of uniform types to the product of two sets, and they obtain a generalized version of Banach's contraction mapping theorem. In this note we prove that these structures are obtained from the usual analogues by means of a particular bijection; hence we do not have a meaningful generalization. For example, this bijection provides, from a result by A. S. Davies, [1], an analogue of Banach's well-known contraction...
On remote points, non-normality and -weight
We show, in particular, that every remote point of is a nonnormality point of if is a locally compact Lindelöf separable space without isolated points and .
On resolvable and irresolvable spaces.
On resolvable spaces and groups
It is proved that every uncountable -bounded group and every homogeneous space containing a convergent sequence are resolvable. We find some conditions for a topological group topology to be irresolvable and maximal.
On rest points of dynamical systems
On restrictive semigroups of continuous functions
On rigid subsets of some manifolds
On rigidity and groups of homeomorphisms
On rings of continuous functions
On rings of Darboux functions
On Rothe's fixed point theorem in a general topological vector space.
On RW-closed sets in topological spaces.
On -closedness and -closedness in topological spaces
On -cluster sets and -closed spaces.
On -metrizable spaces
On saturating ultrafilters on N