On $H$-closed extensions of $\theta$-proximity spaces

In this paper we introduce the concept of extension of a $\theta$-proximity space (see V. V. Fedorchuk, Perfect irreducible mappings and generalized proximities, Math. Sb. (N.S.) 76(118) (1968), 513–536). It is proved that every $\theta$-proximity space has an $H$-closed extension. In the set of $\theta$-proximity $H$-closed extensions of a given $\theta$-proximity space there is a least element.
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