A homological selection theorem implying a division theorem for Q-manifolds

Taras Banakh, and Robert Cauty. "A homological selection theorem implying a division theorem for Q-manifolds." Banach Center Publications 77.1 (2007): 11-22. <http://eudml.org/doc/286370>.

@article{TarasBanakh2007,
abstract = {We prove that a space M with Disjoint Disk Property is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. This implies that the product M × I² of a space M with the disk is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. The proof of these theorems exploits the homological characterization of Q-manifolds due to Daverman and Walsh, combined with the existence of G-stable points in C-spaces. To establish the existence of such points we prove (and afterward apply) homological versions of the Brouwer Fixed Point Theorem and of Uspenskij's Selection Theorem.},
author = {Taras Banakh, Robert Cauty},
journal = {Banach Center Publications},
keywords = {Hilbert cube manifold; disjoint disks property; selection theorems; fixed point theory; -spaces},
language = {eng},
number = {1},
pages = {11-22},
title = {A homological selection theorem implying a division theorem for Q-manifolds},
url = {http://eudml.org/doc/286370},
volume = {77},
year = {2007},
}

TY - JOUR
AU - Taras Banakh
AU - Robert Cauty
TI - A homological selection theorem implying a division theorem for Q-manifolds
JO - Banach Center Publications
PY - 2007
VL - 77
IS - 1
SP - 11
EP - 22
AB - We prove that a space M with Disjoint Disk Property is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. This implies that the product M × I² of a space M with the disk is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. The proof of these theorems exploits the homological characterization of Q-manifolds due to Daverman and Walsh, combined with the existence of G-stable points in C-spaces. To establish the existence of such points we prove (and afterward apply) homological versions of the Brouwer Fixed Point Theorem and of Uspenskij's Selection Theorem.
LA - eng
KW - Hilbert cube manifold; disjoint disks property; selection theorems; fixed point theory; -spaces
UR - http://eudml.org/doc/286370
ER -