STRONG τ-MONOLITHICITY AND FRECHET-URYSOHN PROPERTIES ON Cp(X) Kim, Jun-Hui; Cho, Myung-Hyun;
In this paper, we show that: (1) every strongly -monolithic space X with countable fan-tightness is Frchet-Urysohn; (2) a direct proof of that X is Lindelf when (X) is Frchet-Urysohn; and (3) X is Lindelf when X is paraLindelf and (X) is AP. (3) is a generalization of the result of . And we give two questions related to Frchet-Urysohn and AP properties on (X).
function space;Frchet-Urysohn;AP;-monolithic;strongly -monolithic;countable fan-tightness;Lindelf;
A. V. Arhangel'skii, Some topological spaces that arise in functional analysis Uspekhi Mat. Nauk 31(5) (1976) 17-32. MR 55 #16569, Russian Math. Surveys 31(5) (1976), 14-30.
A. V. Arhangel'skii, Factorization theorems and function spaces: stability and monolithicity, Soviet Math. Dokl. 26 (1982), 177-181.
A. V. Arhangel'skii. Hurewicz spaces, analytic sets and fan-tightness of spaces of functions, Soviet Math. Dokl. 33 (1986), 396-399.
A. V. Arhangel'skii, Topological function spaces, Kluwer Academic Publishers, 1992.
A. Bella and I. V. Yaschenko, On AP and WAP spaces, Comment. Math. Univ. Carolinae, 40(3) (1999), 531-536.
J. Cao, J. Kim, T. Nogura, and Y. Song, Cardinal invariants related to star covering properties, Topology Proc., 26(1) (2001-2002), 83-96.
R. A. McCoy, K-space function spaces, Internat. J. Math. & Math. Sci., 3(4) (1980), 701-711.
V.V. Tkachuk and I.V. Yaschenko, Almost closed sets and topologies they determine, Comment. Math. Univ. Carolinae, 42(2) (2001), 393-403.