Geodesic
Symmetric sequence subspaces of C(α), II
Canadian journal of mathematics, Tome 51 (1999) no. 2, pp. 309-325

Voir la notice de l'article provenant de la source Cambridge University Press

If $\alpha$ is an ordinal, then the space of all ordinals less than or equal to $\alpha$ is a compact Hausdorff space when endowed with the order topology. Let $C(\alpha )$ be the space of all continuous real-valued functions defined on the ordinal interval $[0,\,\alpha ]$ . We characterize the symmetric sequence spaces which embed into $C(\alpha )$ for some countable ordinal $\alpha$ . A hierarchy $\left( {{E}_{\alpha }} \right)$ of symmetric sequence spaces is constructed so that, for each countable ordinal $\alpha$ , ${{E}_{\alpha }}$ embeds into $C\left( {{\omega }^{{{\omega }^{\alpha }}}} \right)$ , but does not embed into $C\left( {{\omega }^{{{\omega }^{\beta }}}} \right)$ for any $\beta \,<\,\alpha$ .
DOI : 10.4153/CJM-1999-016-8
Mots-clés : 03E13, 03E15, 46B03, 46B45, 46E15, 54G12 
Leung, Denny H.; Tang, Wee-Kee. Symmetric sequence subspaces of C(α), II. Canadian journal of mathematics, Tome 51 (1999) no. 2, pp. 309-325. doi: 10.4153/CJM-1999-016-8
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