Boundedly Generated Topological Spaces.
Boundedness in topological spaces
is not subsequential
If a separable dense in itself metric space is not a union of countably many nowhere dense subsets, then its -space is not subsequential.
Canonical embedding of function spaces into the topological bidual of .
Caractérisation topologique de l'espace des fonctions dérivables
Cardinal invariants of -topologies.
Cartesian closed hull for metric spaces
Cartesian closed hull for (quasi-)metric spaces (revisited)
An existing description of the cartesian closed topological hull of , the category of extended pseudo-metric spaces and nonexpansive maps, is simplified, and as a result, this hull is shown to be a special instance of a “family” of cartesian closed topological subconstructs of , the category of extended pseudo-quasi-semi-metric spaces (also known as quasi-distance spaces) and nonexpansive maps. Furthermore, another special instance of this family yields the cartesian closed topological hull of...
Cartesian closed hull of uniform spaces
Cartesian closed topological hull of the construct of closure spaces.
Chain conditions and continuous mappings on
Characterization of Baire-one functions between topological spaces
Characterizing Separability of Function Spaces
Classification of function spaces with the pointwise topology determined by a countable dense set
Classification of spaces of continuous functions on ordinals
We conclude the classification of spaces of continuous functions on ordinals carried out by Górak [Górak R., Function spaces on ordinals, Comment. Math. Univ. Carolin. 46 (2005), no. 1, 93–103]. This gives a complete topological classification of the spaces of all continuous real-valued functions on compact segments of ordinals endowed with the topology of pointwise convergence. Moreover, this topological classification of the spaces completely coincides with their uniform classification.
Classifications and characterizations of Baire-1 functions
Kechris and Louveau in [5] classified the bounded Baire-1 functions, which are defined on a compact metric space , to the subclasses , . In [8], for every ordinal we define a new type of convergence for sequences of real-valued functions (-uniformly pointwise) which is between uniform and pointwise convergence. In this paper using this type of convergence we obtain a classification of pointwise convergent sequences of continuous real-valued functions defined on a compact metric space , and...
Closure-preserving covers in function spaces
It is shown that if admits a closure-preserving cover by closed -compact sets then is finite. If is compact and has a closure-preserving cover by separable subspaces then is metrizable. We also prove that if has a closure-preserving cover by compact sets, then is discrete.
Cofinal families in certain function spaces
Compactifying the space of homeomorphisms
Compactness in the First Baire Class and Baire-1 Operators
For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset of B1 (M,...