On the tightness of chain-net spaces. (English) Zbl 0602.54004

Juhász, István; Weiss, William

Commentat. Math. Univ. Carol. 27, 677-681 (1986).

We give a general construction that yields (in ZFC) (1) a 0-dimensional \(T_ 2\) chain net space of countable tightness that is not sequential; (2) a 0-dimensional \(T_ 2\) chain net space X for which \(t(X)\neq t_ s(X)\). (1) answers a problem of A. V. Arkhangel’skij [Usp. Mat. Nauk 33, No.6(204), 29-84 (1978; Zbl 0414.54002)] and (2) a problem of A. V. Arkhangel’skij, R. Isler and G. Tironi [Commentat. Math. Univ. Carol. 27, 137-154 (1986; Zbl 0587.54007].

MSC:

54A25	Cardinality properties (cardinal functions and inequalities, discrete subsets)
54A20	Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)

Keywords:

sequential space; 0-dimensional \(T_ 2\) chain net space; countable tightness

Citations:

Zbl 0414.54002; Zbl 0587.54007