The existence of continuous weak selections and orderability-type properties in products and filter spaces

Abstract

Orderability, weak orderability and the existence of continuous weak selections on spaces with a single non-isolated point and their products are discussed. We prove that a closed continuous image X of a suborderable space must be hereditarily paracompact provided that its product X × Y with some non-discrete space Y has a separately continuous weak selection.2010 Mathematics Subject Classification. Primary: 54C65; Secondary: 54A20, 54B10, 54B20, 54F05. Key words and phrases. continuous weak selection, weakly orderable space, suborderable space, orderable space, product, space with a single non-isolated point.