On sequential analytic groups

الأصل · EN

We answer a question of S. Todorčević and C. Uzcátegui from TU1 by showing that the only possible sequential orders of sequential analytic groups are 1 and ω₁. Other results on the structure of sequential analytic spaces and their relation to other classes of spaces are given as well. In particular, we provide a full topological classification of sequential analytic groups by showing that all such groups are either metrizable or kω-spaces, which, together with a result by Zelenyuk, implies that there are exactly ω₁ non homeomorphic analytic sequential group topologies.