| چکیده انگلیسی مقاله |
We study some questions related to complete fuzzy metric topological groups. Invariant fuzzy metrics are characterized and we prove that if (G, M, ∗) is a fuzzy metric group such that (M, ∗) is invariant, then a fuzzy metric completion ( ˜ G, ˜ M, ∗) of (G, M, ∗) is a fuzzy metric group and ( ˜ M, ∗) is invariant. Moreover if ( ˜ M, ∗) is an invariant complete metric on (G, τ), then every compatible left invariant (or right invariant) fuzzy metric on G is complete. We also study the so-called three spaces problem: given a fuzzy metric group (G, M, ∗) and a closed normal subgroup N, if one has information about two complete fuzzy metric groups (G, M, ∗), (N, M, ∗) and (G/N, M, ∗), what can be said about the third |
