Cardinal invariants of monotone and porous sets

Abstract

AbstractA metric space (X, d) ismonotoneif there is a linear order < onXand a constantcsuch thatd(x, y)≤c d(x, z)for allx<y<zinX. We investigate cardinal invariants of theσ-idealMongenerated by monotone subsets of the plane. Since there is a strong connection between monotone sets in the plane and porous subsets of the line, plane and the Cantor set, cardinal invariants of these ideals are also investigated. In particular, we show that non(Mon) ≥mσ-linked, but non(Mon) <mσ-centeredis consistent. Also cov(Mon) <cand cof (N) < cov(Mon) are consistent.