We give an example of a Zalcman-type domain in ℂ which is complete with respect to the integrated form of the (k+1)st Reiffen pseudometric, but not complete with respect to the kth one.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-3-5,
author = {Pawe\l\ Zapa\l owski},
title = {Completeness of the inner kth Reiffen pseudometric},
journal = {Annales Polonici Mathematici},
volume = {79},
year = {2002},
pages = {277-288},
zbl = {1021.32003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-3-5}
}
Paweł Zapałowski. Completeness of the inner kth Reiffen pseudometric. Annales Polonici Mathematici, Tome 79 (2002) pp. 277-288. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-3-5/