Concerning Certain Linear Abstract Spaces and Simple Continuous Curves*
نویسنده
چکیده
The first section of this paper is given over mainly to the investigation of linear Hausdorff spaces. However, the principal object of the paper is to characterize topologically that class of point sets used in the geometry for lines, namely, the class of simple continuous curves. This has already been done by R. L. Moore,f by R. L. Wilder, | and by myself.§ The results of this paper generalize the results just referred to mainly by omitting all compactness requirements. As a matter of fact, it will be shown that any nondegenerate linear continuum lying in a Moore space is a simple continuous curve, and that any nondegenerate linear connected subset of a Moore space is homeomorphic with a simple continuous curve.
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