$H$-структуры и $e$-компактификации

The main subject of this paper is notion of $H$-structure introduced in [6] by V.V. Fedorchuk. Recall that an $H$-structure is a family of $\theta$-proximities (see [5] and [4]), and there is a one-to-one correspondence between the set of all $H$-structures on a semiregular Hausdorff space $X$ and the set of all semiregular $H$-closed extensions of $X$. Theorem 2 of this paper shows what restrictions it is necessary to impose on an $H$-structure in order to obtain an $e$-compactification (see [7]) of $X$ Theorem 3 says that the family of all $\theta$-proximities on a semiregular space $X$ forms an $H$-structure on $X$ if $X$ is locally $H$-closed (i. e. every point of $X$ has an open neighbourhood the closure of whitch is $H$-closed). Theorem 1 gives some preliminary characteristics of localy $H$-closed spaces.