Some topological properties weaker than Lindelofness
Some types of points in
Some versions of relative paracompactness and their absolute embeddings
Arhangel’skii [Sci. Math. Jpn. 55 (2002), 153–201] defined notions of relative paracompactness in terms of locally finite open partial refinement and asked if one can generalize the notions above to the well known Michael’s criteria of paracompactness in [17] and [18]. In this paper, we consider some versions of relative paracompactness defined by locally finite (not necessarily open) partial refinement or locally finite closed partial refinement, and also consider closure-preserving cases, such...
Some Wallman compactifications of locally compact spaces
Some weak covering properties and infinite games
We show that (I) there is a Lindelöf space which is not weakly Menger, (II) there is a Menger space for which TWO does not have a winning strategy in the game Gfin(O,Do). These affirmatively answer questions posed in Babinkostova, Pansera and Scheepers [Babinkostova L., Pansera B.A., Scheepers M., Weak covering properties and infinite games, Topology Appl., 2012, 159(17), 3644–3657]. The result (I) automatically gives an affirmative answer of Wingers’ problem [Wingers L., Box products and Hurewicz...
Space of Baire functions. I
Several equivalent conditions are given for the existence of real-valued Baire functions of all classes on a type of -analytic spaces, called disjoint analytic spaces, and on all pseudocompact spaces. The sequential stability index for the Banach space of bounded continuous real-valued functions on these spaces is shown to be either , or (the first uncountable ordinal). In contrast, the space of bounded real-valued Baire functions of class 1 is shown to contain closed linear subspaces with index...
Space structures, their theory and application. II.
Spaces defined by topological games
Spaces for which the diagonal has a closed neighborhood base
Spaces in which compact subsets are closed and the lattice of -topologies on a set
We obtain some new properties of the class of KC-spaces, that is, those topological spaces in which compact sets are closed. The results are used to generalize theorems of Anderson [1] and Steiner and Steiner [12] concerning complementation in the lattice of -topologies on a set .
Spaces of continuous characteristic functions
We show that if is first-countable, of countable extent, and a subspace of some ordinal, then is Lindelöf.
Spaces of continuous functions, -products and Box Topology
For a Tychonoff space , we will denote by the set of its isolated points and will be equal to . The symbol denotes the space of real-valued continuous functions defined on . is the Cartesian product with its box topology, and is with the topology inherited from . By we denote the set can be continuously extended to all of . A space is almost--resolvable if it can be partitioned by a countable family of subsets in such a way that every non-empty open subset of has a non-empty...
Spaces of continuous step functions over LOTS
We investigate spaces over LOTS (linearly ordered topological spaces). We find natural necessary conditions for linear Lindelöfness of over LOTS. We also characterize countably compact LOTS whose is linearly Lindelöf for each n. Both the necessary conditions and the characterization are given in terms of the topology of the Dedekind completion of a LOTS.
Spaces of urelements
Spaces of urelements, II
Spaces related to gamma-sets
Spaces whose connected expansion preserve connected subsets
Spaces with a binary normal subbase
Spaces with a Borel-complete Stone-Čech compactification
Spaces with a locally countable -network.