Hereditarily covering properties of inverse sequence limits

Abstract

Let {X_i, {\pi }_k^i,ω} be an inverse sequence and X = \stackrel{\lim }{\leftarrow }\{X_i,{\pi }_k^i,\omega \}. If each Xi is hereditarily (resp. metaLindelöf, σ-metaLindelöf, σ-orthocompact, weakly suborthocompact, δθ-refinable, weakly θ-refinable, weakly δθ-refinable), then so is X.

Keywords

Inverse sequence limit / hereditarily metaLindelσfness / hereditarily weakly suborthocompactness / hereditarily δθ-refinability / hereditarily weakly θ-refinability / countable product

References

[1] Aoki Y. Orthocompactness of inverse limits and products. Tsukuba J Math, 1980, 4: 241-255

[2] Chiba K. Normality of inverse limits. Math Japonica, 1990, 35(5): 959-970

[3] Chiba K. Covering properties of inverse limits. Questions Answers Gen Topology, 2002, 20: 101-114

[4] Chiba K, Yajima Y. Covering properties of inverse limits II. Topology Proc, 2003, 27(1): 79-100

[5] Engelking R. General Topology (Revised and Completed Ed). Berlin: Heldermann Verlag, 1989

[6] Kemoto N, Smith K D. Hereditary countable metacompactness in finite and infinite product spaces of ordinals. Topology Appl, 1997, 77: 57-63

[7] Kemoto N, Yajima Y. Orthocompactness in products. Tsukuba J Math, 1992, 16(2): 591-596

[8] Yasui Y. Generalized paracompactness. In: Morita K, Nagata J, eds. Topics in General Topology. Amsterdam: North-Holland, 1989

[9] Zhao B. Inverse limits of spaces with the weak B-property. Math J Okayama Univ, 2008, 48: 127-133

[10] Zhu P Y. Hereditarily screenableness and its Tychonoff products. Topology Appl, 1998, 83: 231-238

[11] Zhu P Y. Hereditarily σ-metacompact space and its product properties. Acta Math Sinica (Chin Ser), 1998, 41(3): 531-538 (in Chinese)

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