Abstract:It looks not useful to study the sup = max problem for extent, because there are simple examples refuting the condition. On the other hand, the sup = max problem for Lindel\"of degree does not occur at a glance, because Lindel\"of degree is usually defined by not supremum but minimum. Nevertheless, in this paper, we discuss the sup = max problem for the extent of generalized metric spaces by combining the sup = max problem for the Lindel\"of degree of these spaces.
Keywords: extent, Lindel\"of degree, $\Sigma$-space, strict $p$-space, semi-stratifiable
AMS Subject Classification: 54A25 54D20 03E10 54E18