Topology Proceedings 31 No. 2 (2007), pp. 457-479

Reflective classes of sequentially based convergences, sequential continuity and sequence-rich filters

Szymon Dolecki, Francis Jordan and Frédéric Mynard

We investigate under what conditions sequentially continuous maps between convergence spaces are continuous. Along the way, we provide a new characterization of the Urysohn property for convergence of sequences in terms of a functorial inequality, and introduce a new class of filters, called sequence-rich, intermediate between first-countable and Fréchet a₂.

Keywords: Convergence space, sequential convergence, sequential continuity, continuity, Urysohn convergence, filter

Mathematics Subject Classification: 54A05 54A20 54B30 54C05 54C08 54D55

Document formats: PDF file 220.2 Kb

Topology Proceedings, Volume 31, No. 2 (2007)
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