On a generalized small-object argument for the injective subcategory problem
On accumulation points
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 complexity of metric spaces
On continuous images of almost Tychonoff cubes
On endomorphism semigroups of a fuzzily structured set
On equalizers in the category of frames with weakly open homomorphisms
On essential ring embeddings and the epimorphic hull of .
On extension of functors
A. Chigogidze defined for each normal functor on the category Comp an extension which is a normal functor on the category Tych. We consider this extension for any functor on the category Comp and investigate which properties it preserves from the definition of normal functor. We investigate as well some topological properties of such extension.
On Extension of Functors onto the Kleisli Category of the Inclusion Hyperspace Monad
It is proved that there exists no extension of any non-trivial weakly normal functor of finite degree onto the Kleisli category of the inclusion hyperspace monad.
On extension of functors to the Kleisli category of some weakly normal monads
The problem of extension of normal functors to the Kleisli categories of the inclusion hyperspace monad and its submonads is considered. Some negative results are obtained.
On free topological algebras
On functors of finite degree and -metrizable bicompact 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 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 Limit Permanence of Projectivity and Ingectivity
On linear functorial operators extending pseudometrics
For a functor on the category of metrizable compacta, we introduce a conception of a linear functorial operator extending (for each ) pseudometrics from onto (briefly LFOEP for ). The main result states that the functor of -symmetric power admits a LFOEP if and only if the action of on has a one-point orbit. Since both the hyperspace functor and the probability measure functor contain as a subfunctor, this implies that both and do not admit LFOEP.
On projectively quotient functors
We introduce notions of projectively quotient, open, and closed functors. We give sufficient conditions for a functor to be projectively quotient. In particular, any finitary normal functor is projectively quotient. We prove that the sufficient conditions obtained are necessary for an arbitrary subfunctor of the functor of probability measures. At the same time, any “good” functor is neither projectively open nor projectively closed.