A convex metric for a locally connected continuum
نویسندگان
چکیده
منابع مشابه
A Convex Metric for a Locally Connected Continuum
A subset M of a topological space 5 is said to have a convex metric (even though S may have no metric) if the subspace M of 5 has a convex metric. It is known [5 J that a compact continuum is locally connected if it has a convex metric. The question has been raised [5] as to whether or not a compact locally connected continuum M can be assigned a convex metric. Menger showed [5] that M is conve...
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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...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1949
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1949-09298-4