Abstract
A. K. Steiner undE. F. Steiner described the socalled natural topology κ on spacesA B of transfinite sequences (a β), β∈B,a β∈A [J. Math. Anal. Appl.19, 174–178 (1967)]. These spaces generalize Baire's zerodimensional sequence-spaces. Using these spaces (A B, κ), we generalize two well known theorems of F. Hausdorff, W. Hurewicz, C. Kuratowski and K. Morita on metric spaces and their Lebesgue-dimension respectively, both involving Baire's sequence spaces. Thus we obtain a topological characterization of uniform spaces\((X,\mathfrak{U})\) with a linearly ordered base\(\mathfrak{B}\) of\(\mathfrak{U}\).
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Herrn Professor Dr. N. Hofreiter zum 70. Geburtstag
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Nyikos, P., Reichel, H.C. Uniforme Räume mit einer linear geordneten Basis. Monatshefte fü Mathematik 79, 123–130 (1975). https://doi.org/10.1007/BF01585668
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DOI: https://doi.org/10.1007/BF01585668