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The class of effectively closed infinite-genus surfaces, defining thecompletion of the domain of string perturbation theory, can be included in thecategory $O_G$, which is characterized by the vanishing capacity of the idealboundary. The cardinality of the maximal set of endpoints is shown to be$2^{\mit N}$. The product of the coefficient of the genus-g superstringamplitude in four dimensions by $2^g$ in the $g\to \infty$ limit is anexponential function of the genus with a base comparable in magnitude to theunified gauge coupling. The value of the string coupling is consistent with thecharacteristics of configurations which provide a dominant contribution to afinite vacuum amplitude.Comment: TeX, 33 page

EFFECTIVELY CLOSED INFINITE-GENUS SURFACES AND THE STRING COUPLING