Local connectivity and maps onto non-metrizable arcs

Abstract

Three classes of locally connected continua which admit sufficiently many maps onto non-metric arcs are investigated. It is proved that all continua in those classes are continuous images of arcs and, therefore, have other quite nice properties.

Keywords

• arc
• locally connected continuum
• monotonically normal
• rim-countable
• rim-finite
• rim-metrizable
• rim-scattered.