Baire spaces, -spaces, and some properly hereditary properties.
Base-base paracompactness and subsets of the Sorgenfrey line
A topological space is called base-base paracompact (John E. Porter) if it has an open base such that every base has a locally finite subcover . It is not known if every paracompact space is base-base paracompact. We study subspaces of the Sorgenfrey line (e.g. the irrationals, a Bernstein set) as a possible counterexample.
Behavior of biharmonic functions on Wiener's and Royden's compactifications
Let be a smooth Riemannian manifold of finite volume, its Laplace (-Beltrami) operator. Canonical direct-sum decompositions of certain subspaces of the Wiener and Royden algebras of are found, and for biharmonic functions (those for which ) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.
Bemerkungen über TD-Räume.
Between closed sets and generalized closed sets in closure spaces
The purpose of the present paper is to define and study -closed sets in closure spaces obtained as generalization of the usual closed sets. We introduce the concepts of -continuous and -closed maps by using -closed sets and investigate some of their properties.
Biequivalences and topology in the alternative set theory
Biframe compactifications
Compactifications of biframes are defined, and characterized internally by means of strong inclusions. The existing description of the compact, zero-dimensional coreflection of a biframe is used to characterize all zero-dimensional compactifications, and a criterion identifying them by their strong inclusions is given. In contrast to the above, two sufficient conditions and several examples show that the existence of smallest biframe compactifications differs significantly from the corresponding...
Bijections of scattered spaces onto compact Hausdorff
Bijections onto compact spaces
Binding spaces: A unified completion and extension theory
Bitopological hyperspaces equipped with upper semi-finite snd lower semi-finite topologies
Bitopological local Lindelöfness
Bohr compactifications of discrete structures
We prove the following theorem: Given a⊆ω and , if for some and all u ∈ WO of length η, a is , then a is .We use this result to give a new, forcing-free, proof of Leo Harrington’s theorem: -Turing-determinacy implies the existence of .
Boolean algebras and ultracompactness
Borel extensions of Baire measures
We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasi-Mařík but not Mařík, answering a question of H. Ohta and K. Tamano, and under P(c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space is Mařík,...
Borel extensions of Baire measures in ZFC
We prove: 1) Every Baire measure on the Kojman-Shelah Dowker space admits a Borel extension. 2) If the continuum is not real-valued-measurable then every Baire measure on M. E. Rudin's Dowker space admits a Borel extension. Consequently, Balogh's space remains the only candidate to be a ZFC counterexample to the measure extension problem of the three presently known ZFC Dowker spaces.
Borel-complete topological spaces
Boundaries in digital planes.
Boundaries of and Selectors for Upper Semi-Continuous Multi-Valued Maps.
Buchwalter-Schmets theorems and linear topologies.