Absolutely minimizing Lipschitz extensions on a metric space.
A space X is absolutely strongly star-Hurewicz if for each sequence (Un :n ∈ℕ/ of open covers of X and each dense subset D of X, there exists a sequence (Fn :n ∈ℕ/ of finite subsets of D such that for each x ∈X, x ∈St(Fn; Un) for all but finitely many n. In this paper, we investigate the relationships between absolutely strongly star-Hurewicz spaces and related spaces, and also study topological properties of absolutely strongly star-Hurewicz spaces.
Interrelations between three concepts of terminal continua and their behaviour, when the underlying continuum is confluently mapped, are studied.
We show that AC is equivalent to the assertion that every compact completely regular topology can be extended to a compact Tychonoff topology.