Certain sequences with compact closure (Q1013824)

The authors deal with the question when a \(\beta\)-sequence in a \(T_2\)-space \(X\) has a compact closure. They show that every \(\beta\)-sequence has a feebly compact closure and, if \(X\) is monotonically normal, a compact closure. In regular spaces and in Tychonoff spaces, they give several equivalent conditions for the compactness of the closure of a \(\beta\)-sequence. Further, they express \(\beta\)-sequences with countable closure by fairly concrete forms and give several answers to the question when a \(\beta\)-space is a strong \(\beta\)-space [\textit{Y. Yajima}, Houston J. Math. 33, No.~2, 531--540 (2007; Zbl 1243.54046)]. Examples show the sharpness of the results.