Characterization of locally connected continua in Euclidean spaces

• Date: 1995
• Main Authors: Oleksiv, I. Ya., Олексів, І. Я.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1995
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5504
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove that, for any locally connected bounded continuum in the Euclidean space E n ,n≥2, there exists a sequence of imbeddings of the segment [0, 1] into E n uniformly convergent to a continuous mapping of [0, 1] onto this continuum.