Faisal Ghazi  Al-Sharqi, Majd  Mohammed Abed, Ali. A.  Mhassin, 
    On Polish Groups and their Applications,
    Journal of Engineering and Applied Sciences,
    Volume 13,Issue 18,
    2018,
    Pages 7533-7536,
    ISSN 1816-949x,
    jeasci.2018.7533.7536,
    (https://makhillpublications.co/view-article.php?doi=jeasci.2018.7533.7536)
    Abstract: A top-space X is Polish if it is separable and completely metrizable (com-metrizable) and with Polish topological space G, it is a Polish topological group. In this study, we study new applications of Polish group and new relations with several certain classes of topological spaces such as metrizable space, seprable space, Nagata space and M3-space. If G is a top-gp and (X, dθ) is a separable com-θ-metric space then G is Polish group. If G is a top-gp and X a top-space and each point in X has a neighbourhood which is homeomorphic to an open subset of Rn then G is a Polish group.
    Keywords: Polish group;topological group;metrizable space;separable space;completely metrizable space;M3-space