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We investigate topological AE(0)-groups, a class which contains the class of Polish groups as well as the class of all locally compact groups. We establish the existence of a universal AE(0)-group of a given weight as well as the existence of a universal action of an AE(0)-group of a given weight on an AE(0)-space of the same weight. A complete characterization of closed subgroups of powers of the symmetric group is obtained. It is also shown that every AE(0)-group is Baire isomorphic to a product of Polish groups. These results are obtained by using the spectral descriptions of AE(0)-groups which are presented in Section 3.
Alex Chigogidze. "Topological AE(0)-groups." Fundamenta Mathematicae 167.1 (2001): 79-96. <http://eudml.org/doc/282368>.
@article{AlexChigogidze2001, abstract = {We investigate topological AE(0)-groups, a class which contains the class of Polish groups as well as the class of all locally compact groups. We establish the existence of a universal AE(0)-group of a given weight as well as the existence of a universal action of an AE(0)-group of a given weight on an AE(0)-space of the same weight. A complete characterization of closed subgroups of powers of the symmetric group $S_\{∞\}$ is obtained. It is also shown that every AE(0)-group is Baire isomorphic to a product of Polish groups. These results are obtained by using the spectral descriptions of AE(0)-groups which are presented in Section 3.}, author = {Alex Chigogidze}, journal = {Fundamenta Mathematicae}, keywords = {topological -group; Polish group; inverse spectrum; AE(0)-groups; inverse spectra}, language = {eng}, number = {1}, pages = {79-96}, title = {Topological AE(0)-groups}, url = {http://eudml.org/doc/282368}, volume = {167}, year = {2001}, }
TY - JOUR AU - Alex Chigogidze TI - Topological AE(0)-groups JO - Fundamenta Mathematicae PY - 2001 VL - 167 IS - 1 SP - 79 EP - 96 AB - We investigate topological AE(0)-groups, a class which contains the class of Polish groups as well as the class of all locally compact groups. We establish the existence of a universal AE(0)-group of a given weight as well as the existence of a universal action of an AE(0)-group of a given weight on an AE(0)-space of the same weight. A complete characterization of closed subgroups of powers of the symmetric group $S_{∞}$ is obtained. It is also shown that every AE(0)-group is Baire isomorphic to a product of Polish groups. These results are obtained by using the spectral descriptions of AE(0)-groups which are presented in Section 3. LA - eng KW - topological -group; Polish group; inverse spectrum; AE(0)-groups; inverse spectra UR - http://eudml.org/doc/282368 ER -