Complex sentence: The one-point compactification is compact, contains "X" as an open subspace, and is a Hausdorff space if and only if "X" is locally compact Hausdorff.
Split into simpler sentences: The one-point compactification is compact and contains "X" as an open subspace. It is a Hausdorff space if and only if "X" is locally compact Hausdorff.