Notation in Old Paper

Question

I am reading a paper

http://www.ams.org/journals/bull/1935-41-04/S0002-9904-1935-06049-5/S0002-9904-1935-06049-5.pdf

and I am wondering about the notation in the lemma page which states that

"...there exist a value $n_o$ of n and a sub-interval $[\alpha_0, \beta_0]$ such that $H_{n_0}$ is dense in $H • [\alpha_0, \beta_0]$.

Specifically, what does $H • [\alpha_0, \beta_0]$ mean?

Answer 1

It's the intersection of two sets. Some authors (in old papers, indeed) use $A+B$ for $A\cup B$ and $A\cdot B$ for $A\cap B$. It makes sense when you think of Boolean algebras.