On a construct of closure spaces
On a tensor product in initially structured categories
On binary coproducts of frames
The structure of binary coproducts in the category of frames is analyzed, and the results are then applied widely in the study of compactness, local compactness (continuous frames), separatedness, pushouts and closed frame homomorphisms.
On categories of supertopological spaces
On compactness of lattices.
On compactness with respect to semi-open sets
On continuous maps in closure spaces.
On convergence spaces and groups
On decomposition of fuzzy -continuity.
On -sequentially regular spaces
On extended frames
Some aspects of extended frames are studied, namely, the behaviour of ideals, covers, admissible systems of covers and uniformities.
On generalizations of regular-Lindelöf spaces.
On generalized topological spaces I
We begin a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings. We reformulate the axioms. Generalized topology is found to be connected with the concept of a bornological universe. Both GTS and its full subcategory SS of small spaces are topological categories. The second part of this paper will also appear in this journal.
On generalized topological spaces II
This is the second part of A. Piękosz [Ann. Polon. Math. 107 (2013), 217-241]. The categories GTS(M), with M a non-empty set, are shown to be topological. Several related categories are proved to be finitely complete. Locally small and nice weakly small spaces can be described using certain sublattices of power sets. Some important elements of the theory of locally definable and weakly definable spaces are reconstructed in a wide context of structures with topologies.
On generalized -closed sets.
On Hausdorffness and compactness in intuitionistic fuzzy topological spaces
On hereditary and product-stable quotient maps
It is shown that the quotient maps of a monotopological construct A which are preserved by pullbacks along embeddings, projections, or arbitrary morphisms, can be characterized by being quotient maps in appropriate extensions of A.
On homeomorphic topologies and equivalent set-systems
On lattices of generalized topologies
On minimal separating Boolean algebras.