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arXiv · 2501.11517

Countability conditions in locally solid convergence spaces

Eugene Bilokopytov·Viktor Bohdanskyi·Jan Harm van der Walt
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Abstract

We study (strong) first countability of locally solid convergence structures on Archimedean vector lattices. Among other results, we characterise those vector lattices for which relatively unform-, order-, and $σ$-order convergence, respectively, is (strongly) first countable. The implications for the validity of sequential arguments in the contexts of these convergences are pointed out.

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Eugene Bilokopytov, Viktor Bohdanskyi, Jan Harm van der Walt. 2025-09-18. Countability conditions in locally solid convergence spaces. https://arxiv.org/abs/2501.11517

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