BY continuity of T, (Tx_{n}to Tz) as (ntoinfty).
By continuity in this way we can show that Uk,Nx k ≤ Sk,Nu k.
By continuity in this way, we can show that T U k, i x k * ≤ U k, i x k * for all i = 0, 1,..., N. (3.6).
By continuity in this way, we can show that x n + 1 = K n ( T, N ) x n = U n, N x n ≥ x n for all n ≥ 1.
By continuity in this way, we can show that U k, i x k ≤ x k for all i = 1, 2,..., N. Using (1.9) and (1.11), we get U k, 1 x k - S k, 1 u k = λ k, 1 ( x k - u k ) + ( 1 - λ k, 1 ) ( T x k - T u k ) ≤ 0. Since T is nondecreasing, we have TUk,1x k ≤ TSk,1u k.
Explosion occurs on the set ({tau_{infty}<infty}), because on this set, by continuity of (x t)), (x tau_{infty})=lim_{nrightarrowinfty}x tau_{n})).
Under this definition by continuity, we obtain: x+∞ = +∞ and x−∞ = 0, when 1 < x ≤ +∞.
This time t0 must be positive, by continuity.
We predict that the setpoint for maintaining this basal stress state is affected by continuity of incoming mechanical signals as deformations that activate signalling pathways.
