A basis of the space of continuous function of countable ordinals $C(\alpha) = C [0, \alpha]$ - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T01:33:40Z http://mathoverflow.net/feeds/question/114949 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/114949/a-basis-of-the-space-of-continuous-function-of-countable-ordinals-c-alpha-c A basis of the space of continuous function of countable ordinals $C(\alpha) = C [0, \alpha]$ Amit 2012-11-30T01:31:08Z 2012-11-30T01:31:08Z <p>A basis of the space of continuous function of countable ordinals $C({\alpha}) = C [0, {\alpha}]$, which consist of characteristics functions of clopen subsets of $C({\alpha})$, in some order. But can some one help me to know some details about the cases that how to pick a basis element in successor and in limit ordinal cases, with a example for the space say $C [0, \omega^3]$ or $C [0,\omega^{\omega}]$ .</p>