Topological and Borel compactifications of Polish G-spaces

✍ Scribed by Tzvi Scarr

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 76 KB
• Volume: 105
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00048-6

✦ Synopsis

We investigate the relationships between topological and Borel G-spaces, where G is a Polish group. We show that every Polish G-space can be topologically and equivariantly embedded into a compact Polish G-space iff G is locally compact. This answers a question of Kechris. It also provides a striking contrast to the recent result of Becker and Kechris which states that every Borel G-space can be Borel-embedded into a compact Polish G-space.