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Orthocompactness in infinite product spaces

Authors: Nobuyuki Kemoto and Yukinobu Yajima
Journal: Proc. Amer. Math. Soc. 120 (1994), 591-596
MSC: Primary 54B10; Secondary 54D20
MathSciNet review: 1195724
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Abstract: In this paper, we prove the following results for an infinite product space $ X = \prod\nolimits_{\alpha \in \kappa } {{X_\alpha }} $.

(1) If a dense subspace of $ X$ is orthocompact, then it is $ \kappa $-metacompact.

(2) Assume that all finite subproducts of $ X$ are hereditarily orthocompact. If a subspace of $ X$ is $ \kappa $-metacompact, then it is orthocompact.

References [Enhancements On Off] (What's this?)

  • [Ao] Y. Aoki, Orthocompactness of inverse limits and products, Tsukuba J. Math. 4 (1980), 241-255. MR 623438 (82j:54030)
  • [Ba] D. P. Baturov, Normality in dense subspaces of products, Topology Appl. 36 (1990), 111-116. MR 1068164 (91j:54033)
  • [Be] A. Beślagić, Normality in products, Topology Appl. 22 (1986), 71-82. MR 831182 (87k:54016)
  • [KY] N. Kemoto and Y. Yajima, Orthocompactness in products, Tsukuba J. Math. 16 (1992), 407-422. MR 1200436 (94b:54026)
  • [PP] R. Pol and E. Puzio-Pol, Remarks on Cartesian products, Fund. Math. 93 (1976), 57-69. MR 0428251 (55:1276)
  • [Pr] T. C. Przymusiński, Products of normal spaces, Handbook of Set Theoretic Topology (K. Kunen and J. E. Vaughan, eds.), North-Holland, Amsterdam, 1984, pp. 781-826. MR 776637 (86c:54007)
  • [S1] B. M. Scott, Toward a product theory for orthocompactness, Studies in Topology (N. M. Stavrakas and K. R. Allen, eds.), Academic Press, New York, 1975, pp. 517-537. MR 0372820 (51:9024)
  • [S2] -, More about orthocompactness, Topology Proc. 5 (1980), 155-184. MR 624469 (82h:54029)
  • [Ya] Y. Yajima, A characterization of submetacompactness in terms of products, Proc. Amer. Math. Soc. 112 (1991), 291-296. MR 1054165 (91k:54046)

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Keywords: (Weakly) (sub)metacompact, (weakly) (sub)orthocompact, infinite product, $ \Sigma $-product
Article copyright: © Copyright 1994 American Mathematical Society

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