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.
@article{urn:eudml:doc:43776,
title = {Local connectivity, open homogeneity and hyperspaces.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {6},
year = {1993},
pages = {269-276},
zbl = {0846.54021},
mrnumber = {MR1269757},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:43776}
}
Charatonik, J. J. Local connectivity, open homogeneity and hyperspaces.. Revista Matemática de la Universidad Complutense de Madrid, Tome 6 (1993) pp. 269-276. http://gdmltest.u-ga.fr/item/urn:eudml:doc:43776/