The uniqueness of suspensions over locally connected curves (Q2065109)

The author continues her observations of the uniqueness of various types of continua. The results in the paper are focused on the suspension of a topological space (the suspension \(\text{Sus}(X)\) of a topological space \(X\) is the quotient space defined by \(\text{Sus}(X) = X \times [-1,1] / (X\times \{-1\}, X \times \{1\})\)). The main result of the paper says that if \(X\) is a locally connected curve and the suspension of \(X\), \(\text{Sus}(X)\), is homeomorphic to the suspension of \(Y\), \(\text{Sus}(Y)\), for some continuum \(Y\), then \(X\) and \(Y\) are homeomorphic. This result guarantees that each locally connected curve has a unique suspension. All results in the paper are clearly presented.