The shrinking property of $\Sigma$-products
Yukinobu Yajima · Tsukuba Journal of Mathematics · 1989
YAJIMA COROLLARY 2. A $\Sigma$ -product of paracompact M-spaces has the weak $\mathscr{Q}-$ property.In particular, we have COROLLARY 3. A $\Sigma$ -product of paracompact M-spaces is countably para- compact.Recall that a $\sigma$ -space [14] is a space with a $\sigma$ -locally finite (closed)it is first countable and semi-stratifiable.THEOREM 4. A $\Sigma$ -product of semi-metric spaces is subshrinking.By Proposition 1 and Theorem 4, we have COROLLARY 4. A $\Sigma$ -product of semi-metric spaces is shrinking iff it is normal.