Some problems of Arhangel'skii on diagonal-flexible spaces and rotoids

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• 作者：Fucai Lin ; ^{linfucai2008@aliyun.com" class="auth_mail} ; Kexiu Zhang ^{kxzhang2006@163.com" class="auth_mail} ; Changqing Li ^{helen-smile0320@163.com" class="auth_mail} ; Wei Chen ^{chenwei6808467@126.com" class="auth_mail}
• 关键词：primary ; 22B05 ; 54A25 ; secondary ; 54B05
• 刊名：Topology and its Applications
• 出版年：15 April, 2014
• 年：2014
• 卷：167
• 期：Complete
• 页码：26-30
• 全文大小：223 K

文摘

In this short article, we give complete answers to four problems of Arhangel'skii on diagonal-flexible spaces or rotoids. We list the four problems as follows:

Problem A. Is every compact diagonal-flexible space rectifiable?

Problem B. Is every diagonal-flexible space with a countable 蟺-character first-countable?

Problem C. Is every diagonal-flexible compact space with a countable 蟺-character first-countable?

Problem D. Is every paratopological group a rotoid?