Factorization theorems for extensions of maps
Factorizations of normality via generalizations of -normality
The notion of -normality was introduced and studied by Arhangel’skii, Ludwig in 2001. Recently, almost -normal spaces, which is a simultaneous generalization of -normal and almost normal spaces, were introduced by Das, Bhat and Tartir. We introduce a new generalization of normality, namely weak -normality, in terms of -closed sets, which turns out to be a simultaneous generalization of -normality and -normality. A space is said to be weakly -normal (w-normal if for every pair of disjoint...
Fan-Gottesman type compactification of frames
Fiber orders and compact spaces of uncountable weight
We study an order relation on the fibers of a continuous map and its application to the study of the structure of compact spaces of uncountable weight.
Filter convergence via sequential convergence
Fine convergence in free groups
Fine topologies as examples of non-Blumberg Baire spaces
Fine topology on function spaces.
Finite commutative monoids of open maps
Finite dimensional covers of metric-fine spaces
Finite dimensions defined by means of -coverings
Finite point compactifications of (N, +).
Finite -spaces and universal mappings
Finiteness and compactness in chain-net spaces
First countable and countable spaces all compactifications of which contain βN
First countable spaces without point-countable π-bases
We answer several questions of V. Tkachuk [Fund. Math. 186 (2005)] by showing that ∙ there is a ZFC example of a first countable, 0-dimensional Hausdorff space with no point-countable π-base (in fact, the minimum order of a π-base of the space can be made arbitrarily large); ∙ if there is a κ-Suslin line then there is a first countable GO-space of cardinality κ⁺ in which the order of any π-base is at least κ; ∙ it is consistent to have a first countable,...
First order topology [Book]
Folgenkompaktheit und Auswahlaxiom
Forcing tightness in products of fans
We prove two theorems that characterize tightness in certain products of fans in terms of families of integer-valued functions. We also define several notions of forcing that allow us to manipulate the structure of the set of functions from some cardinal θ to ω, and hence, the tightness of these products. These results give new constructions of first countable <θ-cwH spaces that are not ≤θ-cwH.
Fortsetzbarkeit stetiger Abbildungen und Kompaktheitsgrad topologischer Räume.