Orders of $\pi$-bases

Abstract

We extend the scope of B. Shapirovskii's results [B.E Shapirovskii, "Cardinal invariants in Compact Hausdorff Spaces," Amer. Math. Soc. Transl. (2) Vol. 134, 1987, pp. 93-118] on the order of $\pi$-bases in compact spaces and answer some questions of V. Tkachuk in [V.V. Tkachuk, "Point-countable pi-bases in first-countable and similar spaces," Fund. Math. 186 (2005), pp.55-69].