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This study explores the structure of graphs which together with their complements are edge symmetric.

In the usual development of dimension theory in metric spaces, the equivalence of covering and large inductive dimension plays a central role. In this paper we develope the basic theory of dimension directly from the notion of covering dimension. Several of the basic theorems are extended to non-metrizable spaces. For those results which do require the full strength of metrizability, the proofs are new and rather different from the usual ones. With two minor exceptions, the paper is self-contained.

We present an elementary proof of a transfinite symmetric form of Philip Hall's theorem on systems of distinct representatives and derive some wellknown mapping theorems from it to illustrate the ease with which this form of the theorem may be used.