Sentence examples for m is complete from inspiring English sources

M is complete;   4.

It is obvious that ( X, F, Δ m ) is complete.

It is easy to show that ( S, m ) is complete (see [[45], Lemma 2.1]).

cl(T(F f) ∩ F g))) being subset of cl(T(M)) is complete.

Since M is complete, we deduce that { z n } is convergent as claimed.

Furthermore, ( S, F, Δ M ) is complete iff d is complete.

Since (( X,F,Delta_{M} )) is complete, ({ x_{n} }) is a Cauchy sequence.

A sequence { x n } in X is called a Cauchy sequence, if, for each ϵ ∈ ( 0, 1 ) and t > 0, there exists n 0 ∈ N such that M ( x n, x m, t ) > 1 − ϵ for all n, m ≥ n 0. A sequence { x n } in a fuzzy metric space ( X, M, ∗ ) is said to be convergent to x ∈ X if lim n → ∞ M ( x n, x, t ) = 1 for all t > 0. A 3-tuple ( X, M, ∗ ) is complete if every Cauchy sequence is convergent in X. Lemma 1.6 [7].

Since ( X, d ) is a complete metric space then ( X, M, ∗ ) is complete.

A map T : M → X is said to be semicompact if a sequence {x n } in M such that (x n - Tx n ) → 0 has a subsequence {x j } in M such that x j → z for some z ∈ M. Clearly if cl(T(M)) is compact, then T M) is complete, T(M) is bounded, and T is semicompact.

Hence, C ∞ ( Δ m, ∥ ⋅, …, ⋅ ∥ ) is complete and as such is an n-Banach space.