Abstract
We prove that $\mathscr{K}(Q)$ is a topological group and characterize $\mathscr{K}(Q)$ as a first-category, zero-dimensional, separable, metrizable space of which every non-empty clopen subset is $\Pi_{1}^{1}$-complete. In particular we answer a question of Fujita and Taniyama ([5]). With the additional assumption of Analytic Determinacy it was proved in [5] that $\mathscr{K}(Q)$ is a homogeneous space.
Citation
Henryk Michalewski. "Homogeneity of $\mathscr{K}(Q)$." Tsukuba J. Math. 24 (2) 297 - 302, December 2000. https://doi.org/10.21099/tkbjm/1496164151
Information
