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

Banach Center Publications (2007)

- Volume: 77, Issue: 1, page 11-22
- ISSN: 0137-6934

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topTaras 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 -

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