A compact metric space X̃ is said to be a continuous pseudo-hairy space over a compact space X ⊂ X̃ provided there exists an open, monotone retraction such that all fibers are pseudo-arcs and any continuum in X̃ joining two different fibers of r intersects X. A continuum is called a continuous pseudo-fan of a compactum X if there are a point and a family ℱ of pseudo-arcs such that , any subcontinuum of intersecting two different elements of ℱ contains c, and ℱ is homeomorphic to X (with respect to the Hausdorff metric). It is proved that for each compact metric space X there exist a continuous pseudo-hairy space over X and a continuous pseudo-fan of X.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-2-1,
author = {Janusz R. Prajs},
title = {Continuous pseudo-hairy spaces and continuous pseudo-fans},
journal = {Fundamenta Mathematicae},
volume = {173},
year = {2002},
pages = {101-116},
zbl = {0986.54047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-2-1}
}
Janusz R. Prajs. Continuous pseudo-hairy spaces and continuous pseudo-fans. Fundamenta Mathematicae, Tome 173 (2002) pp. 101-116. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-2-1/