Pointfree forms of Dowker and Michael insertion theorems

• Author(s): Gutiérrez García, Javier ; Kubiak, Tomasz ; Picado, Jorge
• Date: 2007
• Persistent ID: http://hdl.handle.net/10316/11276
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(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
• Document Type: Preprint
• Language: English

Description

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.