Cardinal inequalities using o-free sequences

We introduce the notion of an o-free sequence, related to a free sequence, and show several cardinal inequalities. Modifying recent work of Angelo Bella, we show that if X is a compact Hausdorff space then w(X) =< hL(X)^ot(X). (The o-tightness ot(X), introduced by Tkachenko, has the properties ot(X)=< t(X) and ot(X)=< c(X)). A cardinality bound for compact Hausdorff spaces follows which is shown to be a strict improvement of Arhangel’skii’s well-known bound 2^psi(X). We also give a characterization of the o-tightness in compact Hausdorff spaces using weak o-free sequences.