JP Journal of Geometry and Topology
Volume 1, Issue 2, Pages 163 - 171
(July 2001)
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COMPONENTS AND QUASICOMPONENTS OF SUBSETS OF CONTINUA
B. E. Wilder (USA) and Eric L. McDowell (USA)
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Abstract: In [Amer. Math. Soc. Colloq. Publ., Vol. 28,
Amer. Math. Soc., Providence, R. I., 1942], Whyburn
proves that a continuum, M, is hereditarily
locally connected if and only if the components and
the quasicomponents of any subset of M are
identical. We consider continua for which various
types of subsets have identical classes of
quasicomponents and components, and examine some of
the properties of such continua. In particular, we
prove that a continuum, M, is locally connected
if and only if the components and quasicomponents of
any open subset of M are identical. |
Keywords and phrases: locally connected, component, quasicomponent, aposyndetic. |
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