Openness of induced mappings

✍ Scribed by Janusz J. Charatonik; Wl̵odzimierz J. Charatonik; Alejandro Illanes

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 128 KB
• Volume: 98
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00042-5

✦ Synopsis

Openness of induced mappings between hyperspaces of continua is studied. In particular we investigate continua X such that if for a mapping f :

It is shown that, besides hereditarily locally connected continua, all fans have this property, while some Cartesian products do not have it. If f : X × Y → X denotes the natural projection, then openness of C(f ) implies that X is hereditarily unicoherent. The equivalence holds for dendrites. Some new characterizations of these curves are obtained.