Normal spaces and fixed points of Čech-Stone extensions

✍ Scribed by Michael van Hartskamp; Jan van Mill

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 443 KB
• Volume: 87
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(97)00130-2

✦ Synopsis

We present two examples of nice normal spaces X having the property that for some fixedpoint free homeomorphism on X its tech-Stone extension has a fixed point. One of the spaces presented here is locally countable, locally compact, separable, normal, countably paracompact and weakly zero-dimensional.

The other one is hereditarily normal and strongly zero-dimensional. Our construction of this example however requires the Continuum Hypothesis. Since for paracompact spaces with finite covering dimension every fixed-point free homeomorphism has a fixed-point free tech-Stone extension, these results are "best possible". 0 I998 Elsevier Science B.V.