A note on relative pseudocompactness in the category of frames

Authors

  • Themba Dube

Keywords:

frame, frame homomorphism, real-valued continuous functions on a frame,

Abstract

A subspace $S$ of Tychonoff space $X$ is relatively pseudocompact in $X$ if every $f\in C(X)$ is bounded on $S$. As is well known, this property is characterisable in terms of the functor $\upsilon$ which reflects Tychonoff spaces onto the realcompact ones. A device which exists in the category $\mathbf{CRegFrm}$ of completely regular frames which has no counterpart in $\mathbf{Tych}$ is the functor which coreflects completely regular frames onto the Lindel\"{o}f ones. In this paper we use this functor to characterise relative pseudocompactness. DOI: 10.1017/S000497271200024X

Published

2012-12-17

Issue

Section

Articles