Mikhail Tkachenko (Metropolitan Autonomous University) @ Lecture held in Elysium
Dec 8 @ 6:00 am – 8:00 am

Title: Pseudocompact Paratopological and Quasitopological Groups
by Mikhail Tkachenko (Metropolitan Autonomous University) as part of Topological Groups

Lecture held in Elysium.

Pseudocompactness is an interesting topological property which acquires very specific
features when applied to different algebrotopological objects. A celebrated theorem
of Comfort and Ross published in 1966 states that the Cartesian product of an arbitrary
family of pseudocompact topological groups is pseudocompact. We present a survey
of results related to the validity or failure of the Comfort-Ross’ theorem in the realm of
semitopological and paratopological groups and give some examples showing that
pseudocompactness fails to be stable when taking products of quasitopological groups.