Products of locally compact spaces are k_R-spaces

TL;DR

This paper proves that the product of locally compact Hausdorff spaces is a k_R-space, simplifying the proof of a classical result in topology from 1970.

Contribution

It offers a streamlined proof confirming that products of locally compact Hausdorff spaces are k_R-spaces, extending Noble's theorem from 1970.

Findings

Products of locally compact Hausdorff spaces are k_R-spaces

Simplified proof of Noble's theorem from 1970

All products of locally pseudo-compact k_R-spaces are k_R-spaces

Abstract

A theorem by Norman L. Noble from 1970 asserts that every product of completely regular, locally pseudo-compact k_R-spaces is a k_R-space. As a consequence, all direct products of locally compact Hausdorff spaces are k_R-spaces. We provide a streamlined proof for this fact.