Space S000047
Countable sum of Sierpinski spaces
Also known as: Hjalmar Ekdal topology
Let be the set of positive integers and define a topology by declaring to be open if for every odd , . Equivalently, is closed iff for every even , .
This space is a topological sum of countably-many copies of the Sierpinski space.
Defined as counterexample #55 ("Hjalmar Ekdal Topology") in DOI 10.1007/978-1-4612-6290-9.
A piece of trivia: the origin of the name Hjalmar Ekdal is explained here.