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| 摘要: |
| 本文研究了具有覆盖性质的弱次-ortho-紧空间的σ-积问题,证明存在可数仿紧空间族{Xα:α∈ω1}满足:(1)空间σ{Xα:α∈ω1}的每个有限子乘积是弱次-ortho-紧的;(2)空间σ{Xα:α∈ω1}不是弱次-ortho-紧的.利用拓扑空间乘积性理论,获得了如下结果:设X=σ{Xα:α∈A}是|A|-仿紧空间.如果X的每个有限子乘积是弱次-ortho-紧的,则X也是弱次-ortho-紧的.从而推广了文献[8]的结果. |
| 关键词: σ-积 弱次-ortho-紧 遗传弱次-ortho-紧 |
| DOI： |
| 分类号:O189.11 |
| 基金项目:国家自然科学基金项目(11026081);四川省教育厅科研项目(14ZB0007). |
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| THE WEAKLY SUBORTHOCOMPACTNESS OF σ-PRODUCTS |
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WANG Jian-jun
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| Abstract: |
| In this paper, we discuss the σ-products of weakly suborthocompact spaces characterized by covering. We present that there exists a collection of countably paracompact spaces {Xα:α∈ω1} such that:(1) Each finite subproduct of σ{Xα:α∈ω1} are weakly suborthocompact; (2) The space σ{Xα:α∈ω1} is not weakly suborthocompact. Finally, by using the products of topological spaces, we prove that if X=σ{Xα:α∈A} is a|A|-paracompact space with every finite subproduct of X being weakly suborthocompact, then X is weakly suborthocompact, which generalizes the result in[8]. |
| Key words: σ-product weakly suborthocompact hereditary weakly suborthocompact |
