Colloquium: Behavior of discrete reflexivity in presence of an algebraic structure

Behavior of discrete reflexivity in presence of an algebraic structure

Vladimir Tkachuk, Universidad Autonoma Metropolitana, Mexico City
Friday, April 10 at 3:00 pm
018 Manchester Hall

If P is a topological property, then a space X is called discretely  P if the closure of every discrete subset of X has P. The property P is discretely reflexive in a class A if a space X from A has P if and only if it is discretely P.
I proved in 1988 that compactness is discretely reflexive in the class of all spaces, and it remains an open question whether the Lindelof property is discretely reflexive. However, Arhangel’skii and Buzyakova proved in 1999 that the Lindelof property is discretely reflexive in spaces of countable tightness. In this talk, I will show that:
• Pseudocharacter is discretely reflexive in Lindelof I-groups.
• Countable tightness is not discretely reflexive in hereditarily Lindelof spaces.
Additionally, I will present several results regarding the discrete reflexivity of topological properties in spaces Cp(X).