On function spaces of compact subspaces of Σ-products of the real line
On functors of finite degree and -metrizable bicompact spaces.
On -finitistic spaces and related notions.
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 whitney mappings
On Hausdorff compactifications of non-locally compact spaces.
On Hausdorff intrinsic metric.
On Hausdorff Quotients of Spaces and Magill's Theorem.
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 hit-and-miss hyperspace topologies
The Vietoris topology and Fell topologies on the closed subsets of a Hausdorff uniform space are prototypes for hit-and-miss hyperspace topologies, having as a subbase all closed sets that hit a variable open set, plus all closed sets that miss (= fail to intersect) a variable closed set belonging to a prescribed family of closed sets. In the case of the Fell topology, where consists of the compact sets, a closed set misses a member of if and only if is far from in a uniform sense....
On indecomposability and composants of chaotic continua
A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x,y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that . A homeomorphism f: X → X is continuum-wise expansive if there is c > 0 such that if A is a nondegenerate subcontinuum of X, then there is an integer n ∈ ℤ such that . Clearly, every expansive homeomorphism is continuum-wise expansive, but the converse assertion is not true. In [6], we defined the notion of chaotic continua of homeomorphisms...
On infinite-dimensional manifolds
On inhomogeneity of products of compact F-spaces
On Inverse Limit Of Function Spaces
On lexicographic products
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 local 1-connectedness of Whitney continua
On maps of spaces determined by countable subspaces