$H$-структуры и $e$-компактификации
K. V. Matyushichev Petrozavodsk State University, Faculty of Mathematics
Abstract:
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.
UDC:
515.12
Fulltext:
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