Geodesic
K-Coherence is Cyclicly Extensible and Reducible
Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1270-1276

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

K-coherence (K an integer ≧ –1), has been defined by W. R. R. Transue [3] in such a way that 0-coherence is connectedness and 1-coherence is unicoherence plus local connectedness. It is well-known (see, for instance, [5, p. 82]), that for metric spaces, unicoherence is cyclicly extensible and reducible; furthermore, this result has been generalized by Minear to locally connected spaces, [2, Theorems 4.1 and 4.3]. In this paper we show that for a (k – 1)-coherent and locally (k – 1)-coherent Hausdorff space M,k-coherence is cyclicly extensible and reducible. 
Lehman, B. K-Coherence is Cyclicly Extensible and Reducible. Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1270-1276. doi: 10.4153/CJM-1980-096-5
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