chainable

A simple chain is a finite sequence $L_1, L_2, \cdots,L_n$ of open sets such that L_i intersects L_j if and only if $\vert i-j\vert \leq 1$. The terms of the sequence $L_1, L_2, \cdots,L_n$ are called the links of the chain. An $\varepsilon$-chain is a chain each of whose links has diameter less than $\varepsilon$. a continuum M is chainable if, for each positive number $\varepsilon$, M can be covered by an $\varepsilon$-chain.