More non-analytic classes of continua

The method of [U. Darji, Topology Appl. 103 (2000) 243–248] is extended to get the coanalytic hardness of many classes of metric continua. For instance: (1) the family of all continua in In, n⩾2, that admit only arcs (simple closed curves) as chainable (circularly chainable) subcontinua is coanalytic complete; (2) the family of all continua in In, n⩾2 (n⩾3), which contain no copy of a given nondegenerate chainable (circularly chainable) continuum Y is coanalytic hard; if Y is an arc or a pseudo-arc (a simple closed curve or a pseudo-solenoid), then the family is coanalytic complete; (3) the family of all tree-like continua that contain no hereditarily decomposable subcontinua is coanalytic hard; (4) the family of all λ-dendroids that contain no arcs is coanalytic complete; (5) the sets of all countable-dimensional continua and of all weakly infinite-dimensional continua in the Hilbert cube are coanalytic hard; strongly countable-dimensional continua form a coanalytic complete family.