The Mardešić conjecture for countably compact spaces

Abstract

We shall show that if d and s are positive integers, Ki is a compact linearly ordered topological space for each i<d, X is a countably compact subspace of ∏i<dKi, Zj is an infinite Hausdorff space for each j<d+s, and f:X→∏j<d+sZj is a continuous surjection, then there exist at least s+1-many indexes j<d+s such that Zj is compact and metrizable. This improves the Mardešić Conjecture, which was proved by G. Martínez-Cervantes and G. Plebanek in [1].