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We relate the property of discrete selectivity and its corresponding game, both recently
introduced by VV Tkachuk, to a variety of selection principles and point-picking games. In …

Given a sequence U={U n: n∈ ω} of non-empty open subsets of a space X, a family {V n: n∈
ω} is a shrinking of U if V n is a non-empty open set and V n⊂ U n for every n∈ ω. A space X …

Given a sequence U={U_n: n ∈ ω\} U= U n: n∈ ω of non-empty open subsets of a space X,
a set {x_n: n ∈ ω\} xn: n∈ ω is a selection of UU if x_n ∈ U_n xn∈ U n for every n ∈ ω n∈ …

Let X be a Tychonoff space. We survey some classic and recent results that characterize the
topology or cardinality of X when Cp (X) or Ck (X) is covered by certain families of sets …

We show that, for a Lindelöf Σ-space X, if C p (X,[0, 1]) is strongly dominated by a second
countable space, then X is countable. Under Martin's Axiom we prove that there exists a …

Given a sequence U={U n: n∈ ω} of non-empty open subsets of a space X, a family {V n: n∈
ω} is a shrinking of U if V n is a non-empty open set and V n⊂ U n for every n∈ ω. A space X …

Using binary function spaces, we give an example of a pseudocompact discretely selective
topological group. We show that, under PFA, every compact space of countable tightness …

In this note, we compare and contrast various selective divergence properties such as the
properties of being discretely selective and selectively highly divergent. We identify and …

We establish that an uncountable space X must be essentially uncountable whenever its
extent and tightness are countable. As a consequence, the equality ext (X)= t (X)= ω ext (X) …