Sentence examples for be replaced by continuity from inspiring English sources

The ℳ-continuity of the mappings can be replaced by continuity.

And by Remark 3.1, the ℳ-continuity of the mappings can be replaced by continuity.

Also this condition (i.e. the ICU property of g ( X ) ) is not necessary as it can alternately be replaced by continuity requirements on f and g both.

Also this condition (i.e. the ICU property on g ( X ) ) is not necessary as it can alternately be replaced by continuity requirements on both f and g.

In the context of hypothesis (v), the ICU property on g ( X ) is not necessary as it can alternately be replaced by continuity requirements on f and g both.

We show by counter-example that these distance estimates are not valid in general if the hypothesis of Lipschitz continuity is replaced by continuity.

Note that in Theorem 2.1 the assumption of orbitally G-continuity can be replaced by orbitally continuity, G-continuity or continuity.

Remark 3.16 We note that in Theorem 3.15 the assumption that f is orbitally G-continuous can be replaced by orbital continuity or continuity of f.

From the process of the proof of Theorem 3.1, the monotonicity of ψ in (1.8) can be replaced by the continuity of its.

We also note that the assumption T i n + 1 y n - T i n y n → 0, as n → ∞ and uniform continuity of T i can be replaced by the unform Lipschitz continuity of T i.

The assumption that as can be replaced by the uniform Lipschitz continuity of.