The ε-approximated complete invariance property




complete invariance property (CIP), set of fixed points, Peano continua, α-dense curves, degree of nondensifiability


In the present paper we introduce a generalization of the complete invariance property (CIP) for metric spaces, which we will call the
ε-approximated complete invariance property (ε-ACIP). For our goals, we will use the so called degree of nondensifiability
(DND) which, roughly speaking, measures (in the specified sense) the distance from a bounded metric space to its class of Peano continua.
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.
Also, some essentials differences between the CIP and the ε-ACIP are shown.


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Author Biography

Gonzalo García, UNED

Departamento de Matemáticas


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How to Cite

G. García, “The ε-approximated complete invariance property”, Appl. Gen. Topol., vol. 23, no. 2, pp. 453–462, Oct. 2022.