A tiny peculiar Fréchet space. (English) Zbl 0543.54021

Frič, Roman; Novák, Josef

Czech. Math. J. 34(109), 22-27 (1984).

The authors construct an example of a countable sequentially regular Fréchet space which fails to be regular (X is called sequentially regular) if for each \(f\in C(X) x_ n\to x\Leftrightarrow f(x_ n)\to f(x)\).

Reviewer: A.I.Bashkirov

MSC:

54D55	Sequential spaces
54G20	Counterexamples in general topology
54D10	Lower separation axioms (\(T_0\)–\(T_3\), etc.)

Keywords:

countable sequentially regular Fréchet space

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