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A continuum X is said to be acyclic provided that each
mapping from X into the unit circle
is homotopic to a constant
mapping, i.e., for all mappings
and
there exists a mapping
such that for each
point
we have h(x,0) = f(x) and h(x,1) = c(x).
Janusz J. Charatonik and Pavel Pyrih
2000-09-21