title: Arc-reduced forms for Peano continua.
abstract: Define a point in a topological space to behomotopically fixedif 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 beone-dimensionalif 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.
authors.affiliation: Math Department, Brigham Young University, Provo, UT 84602, USA.
authors.forename: G
authors.initials: G
authors.lastname: Conner
authors.forename: M
authors.initials: M
authors.lastname: Meilstrup
keywords: Homotopy equivalence; One-dimensional; Peano continua; Reduced forms