Every Monotone Open 2-homogeneous Metric Continuum Is Locally Connected
نویسنده
چکیده
In [16, Theorem 3.12, p. 397], Ungar answered a question of Burgess [2] by showing that every 2-homogeneous metric continuum is locally connected. A short, elementary and elegant proof of this result has been given by Whittington [17] who has omitted a powerful result of Effros (viz. Theorem 2.1 of [4, p. 39]) used by Ungar. It is observed in this note that Whittington's proof can be applied to obtain the same conclusion for monotone open 2-homogeneous metric continua. Let a class rot of mappings between topological spaces be given which has the composition property, that is, fo~ every two mappings in rot their composition also is in rot. A topological space X is said to be rot homogeneous provided that for every two points a, b e X there is a
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تاریخ انتشار 2003