Fibrant Extensions and Conditions of Movability


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Abstract

The concept of a fibrant extension of compacta can be used in the study of some properties related to different conditions of movability. For example, “empty” strong shape components of a given compact metric space X correspond to those path components of a fibrant extension X of X which do not intersect X. The fibrant extension X can be constructed as a cotelescope of an ANR-sequence associated with X. Using this representation of X, we prove the following: If a continuum is movable and virtually pointed 1-movable, then it is pointed movable.As a corollary, we get immediately that movable continua, which do not have “empty” strong shape components, are pointed movable. In particular, continua, both fibrant and movable, are of this kind. In fact, they are locally path connected approximate polyhedra.

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