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STRONG τ-MONOLITHICITY AND FRECHET-URYSOHN PROPERTIES ON Cp(X)

• Journal title : Honam Mathematical Journal
• Volume 31, Issue 2,  2009, pp.233-237
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2009.31.2.233
Title & Authors
STRONG τ-MONOLITHICITY AND FRECHET-URYSOHN PROPERTIES ON Cp(X)
Kim, Jun-Hui; Cho, Myung-Hyun;

Abstract
In this paper, we show that: (1) every strongly $\small{{\omega}}$-monolithic space X with countable fan-tightness is Fr$\small{\{e}}$chet-Urysohn; (2) a direct proof of that X is Lindel$\small{\"{o}}$f when $\small{C_p}$(X) is Fr$\small{\{e}}$chet-Urysohn; and (3) X is Lindel$\small{\"{o}}$f when X is paraLindel$\small{\"{o}}$f and $\small{C_p}$(X) is AP. (3) is a generalization of the result of [8]. And we give two questions related to Fr$\small{\{e}}$chet-Urysohn and AP properties on $\small{C_p}$(X).
Keywords
function space;Fr$\small{\{e}}$chet-Urysohn;AP;$\small{{\tau}}$-monolithic;strongly $\small{{\tau}}$-monolithic;countable fan-tightness;Lindel$\small{\"{o}}$f;
Language
English
Cited by
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