Abstract.In the first section of this paper, the notion of a space being rational at a point is generalized to what is here called quasi-rational at a point, ft is shown that a compact metric continuum which is quasi-rational at each point of a dense subset of an open set is both connected im kleinen and semi-locally-connected on a dense subset of that open set. In the second section a Gs set is constructed such that every point in the Gd at which the space is not semi-locally-connected is a cut point. A condition is given for this Gs set to be dense. This condition, in addition to requiring that the space be not semi-locally-connected at any point of a dense Gä set gives a sufficient condition for the space to contain a Gd set of cut points. The condition generalizes that given by Grace.
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