The starting point of this blog post is a slight reformulation of the separation axiom: A topological space is if for all there is a set such that
Given a cardinal , we say that a space is if for all subsets with there is a set such that “splits” , or more formally
Obviously, if and if is , then is also . We say, the space is minimally if it is , but for all cardinals with , the space is not .
Question. Given cardinals , is there a topological space such that and is minimally ?