A NOTE ON RELATIVE PSEUDOCOMPACTNESS IN THE CATEGORY OF FRAMES

作者：Dube Themba^*

来源：Bulletin of the Australian Mathematical Society, 2013, 87(1): 120-130.

DOI：10.1017/S000497271200024X

• frame
• frame homomorphism
• real-valued continuous functions on a frame
• Lindelof coreflection
• relative pseudocompactness

A subspace S of Tychonoff space X is relatively pseudocompact in X if every f is an element of C(X) is bounded on S. As is well known, this property is characterisable in terms of the functor v which reflects Tychonoff spaces onto the realcompact ones. A device which exists in the category CRegFrm of completely regular frames which has no counterpart in Tych is the functor which coreflects completely regular frames onto the Lindelof ones. In this paper we use this functor to characterise relative pseudocompactness.

• 出版日期2013-2