Property Suggestion: F-space and F'-space

[Moniker1998]

Property Suggestion

A space is said to be an $F$-space if two disjoint cozero sets can be completely separated.
It's called an $F'$-space if two disjoint cozero sets have disjoint closures.

Rationale

Most popular is the $F$-space property, but $F'$-spaces have also been extensively studied.

Relationship to other properties

They have relationships to the cozero complemented, basically disconnected and extremally disconnected properties.

Basically disconnected implies $F$-space implies $F'$-space

$F'$-space + cozero complemented implies basically disonnected

[prabau]

Good properties to add