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An example is given to show that there exists a generalized topological space which is irreducible but not β-connected. This gives an answer to Question 2.8 in [6]. Besides, some characterizations of β-connectedness are obtained.  相似文献
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In this paper, we give a minimal system which exhibits distributional chaos of type 1. This is a positive answer to problem (i) in Balibrea and Smítal (2009) [1].  相似文献
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In this note,we present that:(1)Let X=σ{Xα:α∈A} be|A|-paracompact (resp.,hereditarily |A|-paracompact).If every finite subproduct of {Xα:α∈A} has property b1 (resp.,hereditarily property b1),then so is X.(2) Let X be a P-space and Y a metric space.Then,X×Y has property b1 iff X has property b1.(3) Let X be a strongly zero-dimensional and compact space.Then,X×Y has property b1 iff Y has property b1.  相似文献
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In this note,we present that:(1)Let X=σ{Xα:α∈A} be|A|-paracompact (resp.,hereditarily |A|-paracompact).If every finite subproduct of {Xα:α∈A} has property b1 (resp.,hereditarily property b1),then so is X.(2) Let X be a P-space and Y a metric space.Then,X×Y has property b1 iff X has property b1.(3) Let X be a strongly zero-dimensional and compact space.Then,X×Y has property b1 iff Y has property b1.  相似文献
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