Sequentially determined convergence spaces. (English) Zbl 0652.54001

Beattie, R.; Butzmann, H.-P.

Czech. Math. J. 37(112), 231-247 (1987).

From the authors introduction: If \(\lambda\) is a convergence structure and \(\Lambda\) (\(\lambda)\) is the set of all first countable convergence structures having the same convergent sequences, the problem is to choose a “special” convergence structure in \(\Lambda\) (\(\lambda)\). \(\Lambda\) (\(\lambda)\) is a complete lattice with largest and smallest elements. Convergence spaces obtained from the largest element were introduced by Frič and are called sequential. Here the authors study the convergence spaces which arise from the smallest element, which they call sequentially determined.

Reviewer: P.R.Meyer

MSC:

54A20	Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54D55	Sequential spaces

Keywords:

first countable convergence structures; complete lattice

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