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Left $$K$$-completeness in quasi-metric spaces. (English) Zbl 0784.54027
A sequence $$\langle x_ n\rangle$$ in a quasi-pseudo-metric space $$(X,d)$$ is weakly left K-Cauchy provided that for each $$\varepsilon>0$$ there exists $$k\in\mathbb{N}$$ such that $$d(x_ k,x_ n)<\varepsilon$$ whenever $$k\leq n$$. A quasi-pseudo-metric space $$(X,d)$$ is weakly left K- sequentially complete provided that each weakly left K-Cauchy sequence in $$X$$ converges in $${\mathcal T}(d)$$. The author characterizes regular left K- sequentially complete quasi-metric spaces by means of certain bases of countable order. It follows that these spaces are complete Aronszajn spaces.

##### MSC:
 5.4e+16 Uniform structures and generalizations 5.4e+51 Complete metric spaces
##### Keywords:
quasi-pseudo-metric space; Aronszajn spaces
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##### References:
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