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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (1): 87-92    DOI:
    
Some notes on locally (sequentially) connected rectifiable spaces
ZHANG Jing
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China
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Abstract  In this paper, some characterizations of a locally (sequentially) connected rectifiable space $G$ are given under the condition that $G$ is connected, which improves the corresponding result in topological groups; some characterizations of a locally (sequentially) connected rectifiable space $G$ are given from the point of the local neighborhood base of the element e in $G$. It is also proved that if $A$ is a sequentially open subset of a rectifiable space $G$, then $H=\langle A\rangle$ is a sequentially open rectifiable subspace of $G$.

Key words： rectifiable spaces      locally connected spaces      locally sequentially connected spaces      diagonal connected spaces      diagonal sequentially connected spaces     
Received: 07 September 2016      Published: 18 March 2018
CLC:  O189.1  
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ZHANG Jing
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ZHANG Jing. Some notes on locally (sequentially) connected rectifiable spaces. Applied Mathematics A Journal of Chinese Universities, 2017, 32(1): 87-92.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2017/V32/I1/87


关于rectifiable空间中的局部(序列)连通性的几个注记

给出连通的rectifiable空间是局部序列连通(或局部连通)的刻画, 推广了拓扑群中的相应结果; 利用rectifiable空间$G$中$e$的局部邻域基给出$G$是局部连通(或局部序列连通)的刻画; 证明了若$A$是rectifiable空间$G$中的序列开子集, 那么$H=\langle A\rangle$是$G$的序列开rectifiable子空间.

关键词： rectifiable空间,  局部连通空间,  局部序列连通空间,  对角连通空间,  对角序列 
[1] LIN Shou, GE Ying. A note on $csf$-countable spaces[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(1): 79-86.
[2] RONG Yu-yin, XU Luo-shan. Rough homeomorphisms and topological homeomorphisms of generalized approximation spaces[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(3): 315-320.