Arc-reduced forms for Peano continua()

Define a point in a topological space to be homotopically fixed if it is fixed by every self-homotopy of the space, i.e. every self-map of the space which is homotopic to the identity, and define a point to be one-dimensional if it has a neighborhood whose covering dimension is one. In this paper, we show that every Peano continuum is homotopy equivalent to a reduced form in which the one-dimensional points which are not homotopically fixed form a disjoint union of open arcs. In the case of one-dimensional Peano continua, this presents the space as a compactification of a null sequence of open arcs by the homotopically fixed subspace.