Abstract:
We suggest a method for constructing $G$-spaces $X$ such that the semilattice of $G$-compactifications of $X$ coincides with the disjoint union of two semilattices corresponding to partitions of $X$ into subspaces in which the maximal elements are identified. This method is applied to construct examples of $G$-Tychonoff spaces for which the semilattices of equivariant compactifications are of fairly simple structure and contain elements which are minimal but not least.
Keywords:semilattice of $G$-compactifications, Tychonoff space, compact Haudorff space, group action, $G$-Tychonoff space, equipartition, semilattice of equipartititions.
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