Alexandroff compactification

Alexandroff compactification

[al·ik¦san‚drȯf kəm‚pak·tə·fə′kā·shən]
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The end compactification [??] of the hyperbolic disk coincides with the Alexandroff compactification of the [zeta]-plane, which by the stereographic projection (20) is identified with the unit sphere [S.sup.2].
In this setting, it is natural to consider [bar.X] = X [union] [infinity] the Alexandroff compactification of X.
(i) [Omega]* \ E is connected and locally connected (where [Omega]* denotes the Alexandroff compactification of [Omega]), and