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.
Building closed categories
-compactness modulo an ideal.
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.
-points vs -points and -points
In a Tychonoff space , the point is called a -point if every real-valued continuous function on can be extended continuously to . Every point in an extremally disconnected space is a -point. A classic example is the space consisting of the countable ordinals together with . The point is known to be a -point as well as a -point. We supply a characterization of -points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space is a -point....
Calibres, compacta and diagonals
For a space Z let 𝒦(Z) denote the partially ordered set of all compact subspaces of Z under set inclusion. If X is a compact space, Δ is the diagonal in X², and 𝒦(X²∖Δ) has calibre (ω₁,ω), then X is metrizable. There is a compact space X such that X²∖Δ has relative calibre (ω₁,ω) in 𝒦(X²∖Δ), but which is not metrizable. Questions of Cascales et al. (2011) concerning order constraints on 𝒦(A) for every subspace of a space X are answered.
Cantor-connectedness revisited
Following Preuss' general connectedness theory in topological categories, a connectedness concept for approach spaces is introduced, which unifies topological connectedness in the setting of topological spaces, and Cantor-connectedness in the setting of metric spaces.
Caractéristique d'Euler-Poincaré