Almost maximal topologies on groups

Yevhen Zelenyuk. "Almost maximal topologies on groups." Fundamenta Mathematicae 234.1 (2016): 91-100. <http://eudml.org/doc/286177>.

@article{YevhenZelenyuk2016,
abstract = {Let G be a countably infinite group. We show that for every finite absolute coretract S, there is a regular left invariant topology on G whose ultrafilter semigroup is isomorphic to S. As consequences we prove that (1) there is a right maximal idempotent in βG∖G which is not strongly right maximal, and (2) for each combination of the properties of being extremally disconnected, irresolvable, and nodec, except for the combination (-,-,+), there is a corresponding regular almost maximal left invariant topology on G.},
author = {Yevhen Zelenyuk},
journal = {Fundamenta Mathematicae},
keywords = {Stone-Cech compactification; ultrafilter; almost maximal left invariant topology; finite absolute coretract; right maximal idempotent},
language = {eng},
number = {1},
pages = {91-100},
title = {Almost maximal topologies on groups},
url = {http://eudml.org/doc/286177},
volume = {234},
year = {2016},
}

TY - JOUR
AU - Yevhen Zelenyuk
TI - Almost maximal topologies on groups
JO - Fundamenta Mathematicae
PY - 2016
VL - 234
IS - 1
SP - 91
EP - 100
AB - Let G be a countably infinite group. We show that for every finite absolute coretract S, there is a regular left invariant topology on G whose ultrafilter semigroup is isomorphic to S. As consequences we prove that (1) there is a right maximal idempotent in βG∖G which is not strongly right maximal, and (2) for each combination of the properties of being extremally disconnected, irresolvable, and nodec, except for the combination (-,-,+), there is a corresponding regular almost maximal left invariant topology on G.
LA - eng
KW - Stone-Cech compactification; ultrafilter; almost maximal left invariant topology; finite absolute coretract; right maximal idempotent
UR - http://eudml.org/doc/286177
ER -