Galois spaces, representable spaces and strongly locally homogeneous spaces
Generalized analytic spaces, completeness and fragmentability
Classical analytic spaces can be characterized as projections of Polish spaces. We prove analogous results for three classes of generalized analytic spaces that were introduced by Z. Frolík, D. Fremlin and R. Hansell. We use the technique of complete sequences of covers. We explain also some relations of analyticity to certain fragmentability properties of topological spaces endowed with an additional metric.
Generalized Helly spaces, continuity of monotone functions, and metrizing maps
Given an ordered metric space (in particular, a Banach lattice) E, the generalized Helly space H(E) is the set of all increasing functions from the interval [0,1] to E considered with the topology of pointwise convergence, and E is said to have property (λ) if each of these functions has only countably many points of discontinuity. The main objective of the paper is to study those ordered metric spaces C(K,E), where K is a compact space, that have property (λ). In doing so, the guiding idea comes...
Generalized intervals and topology
Generalized linearly ordered spaces and weak pseudocompactness
A space is truly weakly pseudocompact if is either weakly pseudocompact or Lindelöf locally compact. We prove that if is a generalized linearly ordered space, and either (i) each proper open interval in is truly weakly pseudocompact, or (ii) is paracompact and each point of has a truly weakly pseudocompact neighborhood, then is truly weakly pseudocompact. We also answer a question about weakly pseudocompact spaces posed by F. Eckertson in [Eck].
Generalized midset properties characterize geodesic circles and intervals
Geordnete Läuchli Kontinuen
Groupoids, the Phragmen-Brouwer property, and the Jordan curve theorem.
Groups of homeomorphisms and normal subgroups of the group of permutations.