RT Journal Article
T1 Shape index in metric spaces
A1 Romero Ruiz del Portal, Francisco
A1 Salazar, J. M.
AB We extend the shape index, introduced by Robbin and Salamon and Mrozek, to locally defined maps in metric spaces. We show that this index is additive. Thus our construction answers in the affirmative two questions posed by Mrozek in [12]. We also prove that the shape index cannot be arbitrarily complicated: the shapes of q -adic solenoids appear as shape indices in natural modifications of Smale's horseshoes but there is not any compact isolated invariant set for any locally defined map in a locally compact metric ANR whose shape index is the shape of a generalized solenoid. We also show that, for maps defined in locally compact metric ANRs, the shape index can always be computed in the Hilbert cube. Consequently, the shape index is the shape of the inverse limit of a sequence {P n ,g n }  where P n =P  is a fixed ANR and g n =g:P→P  is a fixed bonding map.
PB Polish acad sciences inst mathematics
SN 0016-2736
YR 2003
FD 2003
LK https://hdl.handle.net/20.500.14352/57897
UL https://hdl.handle.net/20.500.14352/57897
DS Docta Complutense
RD 20 ene 2026