On rim-properties of continua (Q2771254)

If \(\mathcal P\) denotes a topological property, then say that a space has \(\text{rim-}\mathcal P\) provided that it has a base of open sets each of whose boundaries has \(\mathcal P\). This is a survey article (no proofs are given) of results concerning rim-finite, rim-countable, rim-metrizable and rim-scattered continua and their images under light mappings. More than a dozen theorems and some examples are cited and the paper ends with a list of five open problems.