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Normality of product spaces. II. (English) Zbl 0699.54004
Topics in general topology, North-Holland Math. Libr. 41, 121-160 (1989).
[For the entire collection see Zbl 0684.00017.]
This is the second part of a survey of normality in products. The first part is by M. Atsuji (see the preceding review). This paper goes into detail about Morita’s P-spaces by proving Morita’s result of 1964 that $$X\times Y$$ is normal for every metric space Y with weight w(Y)$$\leq {\mathfrak m}$$ (where $${\mathfrak m}\geq \aleph_ 0)$$, if and only if X is a normal P($${\mathfrak m})$$-space, and related results. A number of mapping theorems are given. For example, the result of M. E. Rudin and M. Starbird [General Topol. Appl. 5, 235-248 (1975; Zbl 0305.54010)] that if f: $$X\to Y$$ is a closed map, and Z is compact such that $$X\times Z$$ is normal then $$Y\times Z$$ is normal, and the analogous result of A. Bešlagić [Topology Appl. 22, 71-82 (1986; Zbl 0578.54017)] that if f: $$X\to Y$$ is a closed map, and Z is paracompact M-space such that $$X\times Z$$ is collectionwise normal then $$Y\times Z$$ is collectionwise normal. The paper also gives most of what is known about product of normal spaces and Lashnev spaces $$(=$$ closed continuous image of a metric space). For example, T. Hoshina [Fundam. Math. 124, 143-153 (1984; Zbl 0567.54006)] proved that if X is normal and countably paracompact, and Y Lashnev, then $$X\times Y$$ is normal iff it is countably paracompact. Numerous other results are also given. $$\{$$ Taken together, the three survey papers (of Przymusinski, Atsuji and Hoshina) constitute a thorough survey of normality of products up to about 1988$$\}$$.
Reviewer: J.E.Vaughan

##### MSC:
 54B10 Product spaces in general topology 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54-02 Research exposition (monographs, survey articles) pertaining to general topology 54E20 Stratifiable spaces, cosmic spaces, etc.