Abstract
Some consequences of generalized homogeneity are observed in dimension theory of metrizable spaces. In particular, if X X is a connected, locally compact, metric space which is homogeneous with respect to open 0 0 -dimensional mappings and if dim X = n ≥ 1 ( dim X = ∞ ) \dim X = n \geq 1(\dim X = \infty ) , then no subset of dimension ≤ n − 2 \leq n - 2 (respectively, of a finite dimension) separates X X . Thus, homogeneous continua are Cantor manifolds.
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