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

摘要

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 x Y with some non-discrete space Y has a separately continuous weak selection. (C) 2017 Elsevier B.V. All rights reserved.