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acyclic

A continuum

is said to be acyclic provided that each mapping from

into the unit circle $\Bbb S^1$$ is homotopic to a constant mapping, i.e., for all mappings $f: X \to \Bbb S^1$$ and $c: X \to \{p\} \subset \Bbb S^1$$ there exists a mapping $h: X \times [0,1] \to \Bbb S^1$$ such that for each point $x\in X$$ we have

and

Next: almost chainable Up: Definitions Previous: absolutely terminal continuum

Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30