TY - JOUR
AU - García, Gonzalo
PY - 2022/10/03
Y2 - 2024/08/04
TI - The ε-approximated complete invariance property
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 23
IS - 2
SE -
DO - 10.4995/agt.2022.16641
UR - https://polipapers.upv.es/index.php/AGT/article/view/16641
SP - 453-462
AB - <pre>In the present paper we introduce a generalization of the complete invariance property (CIP) for metric spaces, which we will call the<br /> <em>ε-approximated complete invariance property</em> (ε-ACIP). For our goals, we will use the so called <em>degree of nondensifiability</em> <br />(DND) which, roughly speaking, measures (in the specified sense) the distance from a bounded metric space to its class of Peano continua. <br />Our main result relates the ε-ACIP with the DND and, in particular, proves that a densifiable metric space has the ε-ACIP for each ε>0. <br />Also, some essentials differences between the CIP and the ε-ACIP are shown.</pre>
ER -