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On finitely equivalent continua. (English) Zbl 1025.54018
For a positive integer $$n$$, a continuum (that is, a connected compact metric space) is said to be $$n$$-equivalent if it contains exactly $$n$$ topologically distinct (non-degenerate) subcontinua. A continuum is hereditarily $$n$$-equivalent if every subcontinuum is $$n$$-equivalent and is finitely equivalent if it is $$n$$-equivalent for some $$n$$. This paper is a review of results concerning $$n$$-equivalent continua and includes a number of questions and open problems.
##### MSC:
 54F15 Continua and generalizations
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