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

• Accepted : 2009.06.09
• Published : 2009.06.25
• 39 4

#### Abstract

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

#### Keywords

function space;Fr$\'{e}$chet-Urysohn;AP;${\tau}$-monolithic;strongly ${\tau}$-monolithic;countable fan-tightness;Lindel$\"{o}$f

#### References

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