Countable paracompactness of -products

Author:
Le Cheng Yang

Journal:
Proc. Amer. Math. Soc. **122** (1994), 949-956

MSC:
Primary 54B10; Secondary 54D10, 54D20

MathSciNet review:
1216827

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is known that -products of compact spaces always are countably paracompact but not necessarily normal. In the present paper it is proved that a -product of paracompact -spaces is normal if and only if it is countably paracompact.

**[1]**Amer Bešlagić,*Normality in products*, Topology Appl.**22**(1986), no. 1, 71–82. MR**831182**, 10.1016/0166-8641(86)90078-7**[2]**H. H. Corson,*Normality in subsets of product spaces*, Amer. J. Math.**81**(1959), 785–796. MR**0107222****[3]**Geoffrey D. Creede,*Concerning semi-stratifiable spaces*, Pacific J. Math.**32**(1970), 47–54. MR**0254799****[4]**S. P. Gul'ko,*On the properties of*-*products*, Soviet Math. Dokl.**18**(1977), 1438-1442.**[5]**Takao Hoshina,*Products of normal spaces with Lašnev spaces*, Fund. Math.**124**(1984), no. 2, 143–153. MR**774506****[6]**Takao Hoshina,*Shrinking and normal products*, Questions Answers Gen. Topology**2**(1984), no. 2, 83–91. MR**776570****[7]**Takao Hoshina,*Normality of product spaces. II*, Topics in general topology, North-Holland Math. Library, vol. 41, North-Holland, Amsterdam, 1989, pp. 121–160. MR**1053195**, 10.1016/S0924-6509(08)70150-8**[8]**A. P. Kombarov,*On tightness and normality of*-*products*, Soviet Math. Dokl.**19**(1978), 403-407.**[9]**K. Morita,*Note on products of normal spaces with metric spaces*, unpublished.**[10]**Keiô Nagami,*𝜎-spaces and product spaces*, Math. Ann.**181**(1969), 109–118. MR**0244944****[11]**Keiô Nagami,*Countable paracompactness of inverse limits and products*, Fund. Math.**73**(1971/72), no. 3, 261–270. MR**0301688****[12]**-, -*spaces*, Fund. Math.**65**(1969), 169-192.**[13]**Jun-iti Nagata,*Modern general topology*, 2nd ed., North-Holland Mathematical Library, vol. 33, North-Holland Publishing Co., Amsterdam, 1985. MR**831659****[14]**Teodor C. Przymusiński,*Products of normal spaces*, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 781–826. MR**776637****[15]**Mary Ellen Rudin,*Book Review: Aspects of topology // Book Review: Set-theoretic topology: With emphasis on problems from the theory of coverings, zero dimensionality, and cardinal invariants*, Bull. Amer. Math. Soc.**84**(1978), no. 2, 271–272. MR**1567046**, 10.1090/S0002-9904-1978-14471-1**[16]**Mary Ellen Rudin,*The shrinking property*, Canad. Math. Bull.**26**(1983), no. 4, 385–388. MR**716576**, 10.4153/CMB-1983-064-x**[17]**Mary Ellen Rudin and Michael Starbird,*Products with a metric factor*, General Topology and Appl.**5**(1975), no. 3, 235–248. MR**0380709****[18]**Yukinobu Yajima,*On Σ-products of Σ-spaces*, Fund. Math.**123**(1984), no. 1, 29–37. MR**755616****[19]**-,*On*-*products of semi-stratifiable spaces*, Topology Appl.**25**(1987), 1-11.**[20]**Yukinobu Yajima,*The shrinking property of Σ-products*, Tsukuba J. Math.**13**(1989), no. 1, 83–98. MR**1003593****[21]**-,*Subnormality of**and*-*products*, Topology Appl. (to appear).**[22]**Phillip Zenor,*Countable paracompactness in product spaces*, Proc. Amer. Math. Soc.**30**(1971), 199–201. MR**0279769**, 10.1090/S0002-9939-1971-0279769-7

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
54B10,
54D10,
54D20

Retrieve articles in all journals with MSC: 54B10, 54D10, 54D20

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1994-1216827-X

Keywords:
-product,
-space,
countably paracompact,
normal

Article copyright:
© Copyright 1994
American Mathematical Society