@article{García_2022, title={The ε-approximated complete invariance property}, volume={23}, url={https://polipapers.upv.es/index.php/AGT/article/view/16641}, DOI={10.4995/agt.2022.16641}, abstractNote={<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&gt;0. <br />Also, some essentials differences between the CIP and the ε-ACIP are shown.</pre>}, number={2}, journal={Applied General Topology}, author={García, Gonzalo}, year={2022}, month={Oct.}, pages={453–462} }