A note on \(\theta\)-tightness (Q1313213)

Some results involving \(\theta\)-tightness \(t_ \theta\) (introduced by the authors in an earlier paper) are proved. For example: for every subset \(Y\) of a space \(X\) one can find a set \(Z\) in \(X\) such that \(Y \subset Z\), \(| Z| \leq | Y|^{t_ \theta (X)}\) and any two disjoint \(\theta\)-closed subsets of \(Z\) have disjoint \(\theta\)- closures in \(X\).