On the lattice structure of topologies
On the structure of perfect sets in various topologies associated with tree forcings
We prove that the Ellentuck, Hechler and dual Ellentuck topologies are perfect isomorphic to one another. This shows that the structure of perfect sets in all these spaces is the same. We prove this by finding homeomorphic embeddings of one space into a perfect subset of another. We prove also that the space corresponding to eventually different forcing cannot contain a perfect subset homeomorphic to any of the spaces above.
On the topology generated by preopen sets
On --open sets and a decomposition of almost--continuity.
On -resolvable and almost--resolvable spaces
We continue the study of almost--resolvable spaces beginning in A. Tamariz-Mascar’ua, H. Villegas-Rodr’ıguez, Spaces of continuous functions, box products and almost--resoluble spaces, Comment. Math. Univ. Carolin. 43 (2002), no. 4, 687–705. We prove in ZFC: (1) every crowded space with countable tightness and every space with -weight is hereditarily almost--resolvable, (2) every crowded paracompact space which is the closed preimage of a crowded Fréchet space in such a way that the...
Operators associated to a topology over a set and related notions.
-topological and -regular: Dual notions in convergence theory.
Partial discretization of topologies
In questo lavoro daremo una construzione che aumenta il numero di sottospazi chiusi e discreti dello spazio e daremo alcune applicazioni di tale construzione.
Pointwise density topology
The paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue measurable set does not need to be measurable and the set of pointwise density points of a set having the Baire property does not need to have the Baire property. However, the set of pointwise density...
Products of Minimal Abelian Groups.
Properties of some -dense-in-itself subsets.
Properties of -expansions of topologies.
Proximity classes of uniformities
Pseudocompact refinements of compact group topologies.
Pseudouniform topologies on given by ideals
Given a Tychonoff space , a base for an ideal on is called pseudouniform if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on converges uniformly to the same limit. This paper focuses on pseudouniform bases for ideals with particular emphasis on the ideal of compact subsets and the ideal of all countable subsets of the ground space.
Quasiorders, principal topologies, and partially ordered partitions.
Regular-uniform convergence and the open-open topology.
Relations between some topologies
Relative compactness and recent common generalizations of metric and locally compact spaces
Remarks on locally closed sets.