https://en.wikipedia.org/wiki/Limit_point_compact Limit point compact In mathematics, a topological space X is said to be limit point compact[1][2] or weakly countably compact[3] if every infinite subset of X has a limit point in X. This property generalizes a property of compact spaces. In a metric space, limit point compactness, compactness, and sequential compactness are all equivalent. For general topological spaces, however, these three notions of compactness are not equivalent.
References 1. Nagata, J.-I. (1985), Modern General Topology, North-Holland Mathematical Library (3rd ed.), Elsevier, p. 104, https://books.google.co.jp/books?id=ecvd8dCAQp0C&pg=PA104&redir_esc=y#v=onepage&q&f=false
https://en.wikipedia.org/wiki/Jun-iti_Nagata Jun-iti Nagata (長田 潤一,1925 - 6 November 2007) was a Japanese mathematician specializing in topology. https://upload.wikimedia.org/wikipedia/commons/thumb/8/86/Jun-iti_Nagata.jpg/330px-Jun-iti_Nagata.jpg Jun-iti Nagata in 1977
