Dikranjan, D.; Gotchev, I. Sequentially closed and absolutely closed spaces. (English) Zbl 0654.54016 Boll. Unione Mat. Ital., VII, Ser., B 1, 849-860 (1987). Let \({\mathcal P}\) be a category of spaces. A \({\mathcal P}\)-space is \({\mathcal P}\)- closed (respectively, sequentially \({\mathcal P}\)-closed, absolutely \({\mathcal P}\)-closed) if X is closed (respectively, sequentially closed, the equalizer of two continuous functions into a \({\mathcal P}\)-space) in every \({\mathcal P}\)-space in which X can be embedded. A space is US (respectively, SUS) if every convergent sequence in X has a unique limit point (respectively, cluster point). A US (respectively, SUS) space X is sequential US-closed (respectively, SUS-closed) iff X is sequentially (respectively, countably) compact. An absolutely US-closed space is sequentially US-closed, but the converse is false; a SUS-space is absolutely SUS-closed iff it is sequentially SUS-closed. Also, an US- closed (respectively, SUS-closed) space is finite (respectively, compact). Reviewer: J.R.Porter Cited in 4 Documents MSC: 54D25 “\(P\)-minimal” and “\(P\)-closed” spaces Keywords:absolutely US-closed space; sequentially US-closed PDFBibTeX XMLCite \textit{D. Dikranjan} and \textit{I. Gotchev}, Boll. Unione Mat. Ital., VII. Ser., B 1, 849--860 (1987; Zbl 0654.54016)