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On extension of functors

L. Karchevska, Taras Radul (2012)

Commentationes Mathematicae Universitatis Carolinae

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 generalized topological spaces II

Artur Piękosz (2013)

Annales Polonici Mathematici

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

Friedhelm Schwarz, Sibylle Weck-Schwarz (1992)

Commentationes Mathematicae Universitatis Carolinae

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.

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