## A necessary and sufficient condition for the metricization of a topological space |

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Aeronautics and Space Akademii Nauk SSSR Aleksandrov and P. S. ascribed to previous author submits cized closure compact spaces CONDITION FOR THEMETRICIZATION continuous function countable basis defects ascribed denote Doklady Akademii Nauk dostatochnoye usloviye metrizuyemosti F-192 National Aeronautics finite coverings 7n finite number free of defects Hausdorf space homeomorphic intersects lation from Doklady lemma locally finite covering locally metriciz mapping f Math metric space metricization problem metricization theorem metrizuyemosti topologicheskogo prostranstva NASA NASA TT NASA TECHNICAL TRANSLATION NECESSARY AND SUFFICIENT neighborhood Ox Neobkhodimoye i dostatochnoye number of elements open set OTS price OTS prrie P. S. Aleksandrov P. S. Uryson pairs paracompact point x€R previous solutions regular space set of locally Smirnov Space Administration space HT SUFFICIENT CONDITION take a neighborhood TECHNICAL TRANSLATION F-192 theorem of P. S. topological mapping TOPOLOGICAL SPACE Trans TT F-192 National usloviye metrizuyemosti topologicheskogo USSR