Clones in topology and algebra.
Closed and open sets in topologies induced by lattice ordered vector groups
Closed, continuous images of complete metric spaces
Closed copies of the rationals
Closed discrete subsets of separable spaces and relative versions of normality, countable paracompactness and property
In this paper we show that a separable space cannot include closed discrete subsets which have the cardinality of the continuum and satisfy relative versions of any of the following topological properties: normality, countable paracompactness and property . It follows that it is consistent that closed discrete subsets of a separable space which are also relatively normal (relatively countably paracompact, relatively ) in are necessarily countable. There are, however, consistent examples of...
Closed embeddings into complements of -products
In some sense, a dual property to that of Valdivia compact is considered, namely the property to be embedded as a closed subspace into a complement of a -subproduct of a Tikhonov cube. All locally compact spaces are co-Valdivia spaces (and only those among metrizable spaces or spaces having countable type). There are paracompact non-locally compact co-Valdivia spaces. A possibly new type of ultrafilters lying in between P-ultrafilters and weak P-ultrafilters is introduced. Under Martin axiom and...
Closed graph multi-selections
A classical Lefschetz result about point-finite open covers of normal spaces is generalised by showing that every lower semi-continuous mapping from a normal space into the nonempty compact subsets of a metrizable space admits a closed graph multi-selection. Several applications are given as well.
Closed ideals in semigroups of continuous selfmaps.
Closed ideals in topological algebras: a characterization of the topological -algebra
Let be a uniformly closed and locally m-convex -algebra. We obtain internal conditions on stated in terms of its closed ideals for to be isomorphic and homeomorphic to , the -algebra of all the real continuous functions on a normal topological space endowed with the compact convergence topology.
Closed mapping theorems on -spaces with point-countable -networks
We prove some closed mapping theorems on -spaces with point-countable -networks. One of them generalizes Lašnev’s theorem. We also construct an example of a Hausdorff space with a countable base that admits a closed map onto metric space which is not compact-covering. Another our result says that a -space with a point-countable -network admitting a closed surjection which is not compact-covering contains a closed copy of .
...-Closed Mappings.
Closed mappings and local dimension
Closed mappings and the Freudenthal compactification
Closed mappings are open at a set
Closed mappings on complete metric spaces
Closed mappings which lower dimension
Closed retractions of Euclidean spaces
Closed subgroups in Banach spaces
We show that zero-dimensional nondiscrete closed subgroups do exist in Banach spaces E. This happens exactly when E contains an isomorphic copy of . Other results on subgroups of linear spaces are obtained.
Closed subsets of absolutely star-Lindelöf spaces II
In this paper, we prove the following two statements: (1) There exists a discretely absolutely star-Lindelöf Tychonoff space having a regular-closed subspace which is not CCC-Lindelöf. (2) Every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented in a Hausdorff (regular, Tychonoff) absolutely star-Lindelöf space as a closed subspace.
Closed subsets of star -compact spaces