On nondiscreteness of a higher topological homotopy group and its cardinality

Ghane, H. ; Hamed, Z.

Bull. Belg. Math. Soc. Simon Stevin, Tome 16 (2009) no. 1, p. 179-183 / Harvested from Project Euclid

Résumé

Here, we are going to extend Mycielski's conjecture to higher homotopy groups. Also, for an $(n-1)$-connected locally $(n-1)$-connected compact metric space $X$, we assert that $\pi^{top}_{n}(X)$ is discrete if and only if $\pi_{n}(X)$ is finitely generated. Moreover, $\pi^{top}_{n}(X)$ is not discrete if and only if it has the power of the continuum.

Détail

Publié le : 2009-02-15
Classification:  Topological homotopy group,  $n$-semilocally simply connected space,  $n$-connected space,  locally $n$-connected space,  55Q05,  55U40,  54H11,  55P35