# Free locally convex spaces with a small base

@article{Gabriyelyan2016FreeLC,
title={Free locally convex spaces with a small base},
author={S. Gabriyelyan and J. Kakol},
journal={Revista de la Real Academia de Ciencias Exactas, F{\'i}sicas y Naturales. Serie A. Matem{\'a}ticas},
year={2016},
volume={111},
pages={575-585}
}
• Published 2016
• Mathematics
• Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
• The paper studies the free locally convex space L(X) over a Tychonoff space X. Since for infinite X the space L(X) is never metrizable (even not Fréchet-Urysohn), a possible applicable generalized metric property for L(X) is welcome. We propose a concept (essentially weaker than first-countability) which is known under the name a $$\mathfrak {G}$$G-base. A space X has a $$\mathfrak {G}$$G-base if for every $$x\in X$$x∈X there is a base $$\{ U_\alpha : \alpha \in \mathbb {N}^\mathbb {N}\}$${U… CONTINUE READING

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