A cyclic monotonically normal space which is not \(K_ 0\). (English) Zbl 0789.54027

Rudin, Mary Ellen

Proc. Am. Math. Soc. 119, No. 1, 303-307 (1993).

The author constructs a remarkable example of a cyclic monotonically normal space \(T\) wich is not a \(K_ 0\)-space. \(T\) is the first example in ZFC of a \(K_ 1\)-space which is not \(K_ 0\). Furthermore, \(T\) is a very nice space: \(T\) is first countable, 0-dimensional, hereditarily separable and hereditarily Lindelöf. (A few subscript misprints on p. 306: On line 12, replace \(y\) by \(j\) and the first two \(r\)’s by \(p\)’s; on line 13 replace \(y\) by \(j\); the first question at the bottom of the page should be “Does there exist a compact \(K_ 1\)-space which is not \(K_ 0\)?” Also, on line 1 of p. 305, replace \(\{y^ 1,y^ 2,y^ 3\}\) by \(\{y^ 0,y^ 1,y^ 2\})\).

Reviewer: C.R.Borges (Davis)

MSC:

54D15

Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)

Keywords:

\(K_ 0\)-space; \(K_ 1\)-space; monotonically normal space