Electronic Version 18 (1993), 221-229

Zhu Peiyong

In 1991, T. Hui and K. Chiba investigated the various covering properties of \sigma-products. They obtained the following results:

1. Let X = \sigma{ X_\alpha : \alpha \in A }. If every finite subproduct of X is metacompact, then X is metacompact.

2. Let X = { X_\alpha : \alpha \in A }. If every finite subproduct of X is subparacompact and X is subnormal, then X is subparacompact.

3. Let X = \sigma{ X_\alpha : \alpha \in A } and X is normal. If every finite subproduct of X is submetacompact, then X is submetacompact.

In this paper, we first prove that \sigma-product of metalindelöf spaces has the result which is similar to (A). Secondly, we discuss Tychonoff product of two metalindelöf spaces on the basis of ([3], Theorem 6.25). The following two results are obtained:

(i) Suppose X is a P-space and Y is a strong \Sigma-space. If X and Y are both metalindelöf space then X ×Y is also metalindelöf.

(ii) Let X be metalindelöf P-space, Y has a point-countable base, then X ×Y is metalindelöf.

• AtlasImage format
• HTML version (with inline images)
• DVI file
• PostScript file

volume 18: table of contents
topology proceedings Electronic Version