Simply connected partitions of one-dimensional and planar continuous curves

This dissertation presents extensions to theorems of R. H. Bing concerning partitions of continuous curves. The existence of [element of]-partitions, [element of]-[cursive S]-partitions, and brick partitions, each of whose members is simply connected, is shown for continuous curves in E[lowered 2] that have a countable basis of simply connected open sets and for one-dimensional continuous curves that have a countable basis of simply connected open sets. The existence of decreasing sequences of [element of]-partitions, [element of]-[cursive S]-partitions, and brick partitions, each of whose members is simply connected, is shown for continuous curves in E[lowered 2] that have a countable basis of simply connected open sets and for one-dimensional continuous curves that have a countable basis of simply connected open sets. It is also shown that if a continuous curve in E[lowered 2] or a one-dimensional continuous curves has a countable basis of simply connected open sets, then it has a countable basis of simply connected open sets whose subintersections are simply connected.