Shrinking property in \(\Sigma\)-products of paracompact p-spaces
This paper is devoted to the study of the shrinking property of a \(\Sigma\)-product of spaces; a space is said to have the shrinking property if for every open cover \(\{U_{\lambda}| \lambda \in \Lambda \}\) there exists an open cover \(\{V_{\lambda}| \lambda \in \Lambda \}\) with \(\bar V_{\lambda}\subset U_{\lambda}\) for each \(\lambda\in \Lambda\). The main result is that a \(\Sigma\)-product of paracompact p-spaces with countable tightness has the shrinking property. As a corollary, by using a theorem of \textit{A. P. Kombarov} [Sov. Math., Dokl. 19, 403-407; Dokl. Akad. Nauk SSSR 239, 775-778 (1978; Zbl 0397.54013)] it is also mentioned that a \(\Sigma\)-product of paracompact p-spaces has the shrinking property iff it is normal.
paracompact p-spaces with countable tightness
scientific article; zbMATH DE number 3921496