A property of hereditarily locally connected continua related to arcwise accessibility

Journal of the Australian Mathematical Society

Joseph N. Simone¹ 

关键词: 54 F 15;    54 D 05;   

DOI  :  10.1017/S144678870003891X

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

A continuum (that is, a compact connected Hausdorff space) is hereditarily locally connected if each of its subcontinua is locally connected. It is shown that a continuum X is hereditarily locally connected if and only if for each connected open set U in X and each point p in the boundary of U, U ∪ {p} is locally connected. This result is used to prove that if X is an hereditarily locally connected continuum, U is a connected open subset of X, p is an element of the boundary of U and X is first countable at p, then p is arcwise accessible from U.

【 授权许可】

Unknown