Full paper in PDF:
$%J. J. Charatonik, Local connectivity, open homogeneity, and hyperspaces, Rev. Mat. Univ. Complut. Madrid 6 (1993), no. 2, 269–276.%$

Local Connectivity, Open Homogeneity, and Hyperspaces
Janusz J. CHARATONIK
Mathematical Institute
University of Wroclaw
Pl. Grudwaldzki 2/4
50-384 Wroclaw — Poland

Received: October 19, 1992
Revised: March 22, 1993
ABSTRACT

In the first part of the paper behavior of conditions related to local connectivity at a point is discussed if the space is transformed under a mapping that is interior or open at the considered point of the domain. The second part of the paper deals with metric locally connected continua. They are characterized as continua for which the hyperspace of their nonempty closed subjects is homogeneous with respect to open mappings. A similar characterization for the hyperspace of subcontinua remains an open question.

2000 Mathematics Subject Classification: 54B20, 54C50, 54F15.