The class of locally connected and locally homeomorphically homogeneous topological spaces such that every one-to-one continuous mapping of an open subspace into the space is open has been considered. For a foliation F [3] on a Sikorski differential space M with leaves having the above properties it is proved that for some open sets U in M covering the set of all points of M the connected components of U ∩ L̲ in the topology of M coincide with the connected components in the topology of L for L∈ F.
@article{bwmeta1.element.bwnjournal-article-apmv54z2p179bwm,
author = {W\l odzimierz Waliszewski},
title = {On foliations in Sikorski differential spaces with Brouwerian leaves},
journal = {Annales Polonici Mathematici},
volume = {55},
year = {1991},
pages = {179-182},
zbl = {0723.57022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv54z2p179bwm}
}
Włodzimierz Waliszewski. On foliations in Sikorski differential spaces with Brouwerian leaves. Annales Polonici Mathematici, Tome 55 (1991) pp. 179-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv54z2p179bwm/
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[001] [2] W. Waliszewski, Regular and coregular mappings of differential spaces, Ann. Polon. Math. 30 (1975), 263-281. | Zbl 0309.58004
[002] [3] W. Waliszewski, Foliations of differential spaces, Demonstratio Math. 18 (1) (1985), 347-352. | Zbl 0613.58002