Pointfree forms of Dowker and Michael insertion theorems

• Autor(es): Gutiérrez García, Javier ; Kubiak, Tomasz ; Picado, Jorge
• Data: 2007
• Identificador Persistente: http://hdl.handle.net/10316/11276
• Origem: Estudo Geral - Universidade de Coimbra
• Assunto(s): Frame; Sublocale; Insertion theorem; Extension theorem; Kat¡etov relation; Continuous real function on a frame; Lower semicontinuous; Upper semicontinuous; Normal frame; Perfectly normal frame; Countably paracompact frame
• Tipo de Documento: Preprint
• Idioma: Inglês

Descrição

In this paper we prove two strict insertion theorems for frame homomorphisms. When applied to the frame of all open subsets of a topological space they are equivalent to the insertion statements of the classical theorems of Dowker and Michael regarding, respectively, normal countably paracompact spaces and perfectly normal spaces. In addition, a study of perfect normality for frames is made. Ministry of Education and Science of Spain and FEDER under grant MTM2006-14925-C02-02. The third named author acknowledges financial support from the Centre of Mathematics of the University of Coimbra/FCT.