Glasnik Matematicki, Vol. 37, No.2 (2002), 365-373.
SMOOTHNESS IN n-FOLD HYPERSPACES
Sergio Macias and Sam B. Nadler, Jr.
Instituto de Matematicas,
Circuito Exterior, Ciudad Universitaria, Mexico,
D.F., C.P. 04510, Mexico
e-mail: macias@servidor.unam.mx
Department of Mathematics,
West Virginia University, Morgantown, WV, 26506-6310, USA
e-mail: nadler@math.wvu.edu
Abstract. We prove that
C*-smoothness
of a homogeneous continuum implies its indecomposability. We define the
analogue of
C*-smoothness
for n-fold hyperspaces and
investigate its relation to
C*-smoothness.
We characterize the class of hereditarily indecomposable continua in
terms of
Cn*-smoothness.
2000 Mathematics Subject Classification.
54B20.
Key words and phrases. Continuum,
Cn*-smoothness,
decomposable continuum, hereditarily indecomposable continuum,
homogeneous continuum, irreducible continuum, indecomposable
continuum, n-fold hyperspace, order arc, unicoherent
continuum.
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