ИСТИНА

Suppose G is a topological group and H is a closed subgroup of G. Then G/H is the quotient space of G, that is, members of G/H are left cosets xH, where x from G, and the topology is the quotient topology. The space G/H is homogeneous. Theorem. Every remainder of any paracompact sigma-space is metric-friendly. A coset space G/H is compactly-fibered if H is compact. Theorem. For every compactly-fibered coset space X=G/H, either each remainder of X is metric-friendly, or each remainder of X is pseudocompact. Theorem. Suppose X is a compactly-fibered coset space, and Y=bX\X is a remainder of X. Then the following conditions are equivalent: (1) Y is metacompact; (2) Y is paralindelöf; (3) Y is Dieudonné complete; (4) Y is Lindelöf; (5) Y is metric-friendly.