On finitely equivalent continua (Q1811968)

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.