@techreport{e1d3653cc51a4e32a35ec969f21a95f7,

title = "The $κ$-Fr{\'e}chet--Urysohn property for locally convex spaces",

abstract = " A topological space $X$ is $\kappa$-Fr\'{e}chet--Urysohn if for every open subset $U$ of $X$ and every $x\in \overline{U}$ there exists a sequence in $ U$ converging to $x$. We prove that every $\kappa$-Fr\'{e}chet--Urysohn Tychonoff space $X$ is Ascoli. We apply this statement and some of known results to characterize the $\kappa$-Fr\'echet--Urysohn property in various important classes of locally convex spaces. In particular, answering a question posed in [7] we obtain that $C_p(X)$ is Ascoli iff $X$ has the property $(\kappa)$. ",

keywords = "math.GN, math.FA, 46A03, 46A08, 54C35",

author = "S. Gabriyelyan",

year = "2018",

language = "אנגלית",

series = "Arxiv preprint",

edition = " arXiv:1812.10166 [math.GN]",

type = "WorkingPaper",

}