## Tsukuba Journal of Mathematics

### Homogeneity of $\mathscr{K}(Q)$

Henryk Michalewski

#### 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.

#### Article information

Source
Tsukuba J. Math., Volume 24, Number 2 (2000), 297-302.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496164151

Digital Object Identifier
doi:10.21099/tkbjm/1496164151

Mathematical Reviews number (MathSciNet)
MR1818088

Zentralblatt MATH identifier
0987.54044

#### Citation

Michalewski, Henryk. Homogeneity of $\mathscr{K}(Q)$. Tsukuba J. Math. 24 (2000), no. 2, 297--302. doi:10.21099/tkbjm/1496164151. https://projecteuclid.org/euclid.tkbjm/1496164151