For each x ∈ C, define the mapping G : C → 2 C by G ( x ) = { y ∈ C : f ( x, y ) ≤ λ }, which is closed by hypothesis (1).
Since T : ⋃ n ∈ Z 0 + A 0 n → ⋃ n ∈ Z 0 + B 0 n and lim n → ∞ A n ⊆ lim n → ∞ A 0 n, so that y ∈ lim n → ∞ A 0 n, since ⋂ n ≥ m A 0 n is closed by hypothesis for some m ∈ Z 0 + and lim n → ∞ A 0 n is also closed.
As a result, since ⋃ n = 0 ∞ A 0 n is non-empty and closed, any infinite union of non-empty closed sets ⋃ n = k ∞ A 0 n is also non-empty and closed for any k ∈ Z 0 + since ⋃ n = 0 ∞ A 0 n is assumed to be closed by hypothesis and it is trivially non-empty.
Corn oil was considered interesting for this study because it derives, as a residue, from the bioethanol industrial production, thus to close the hypothesis to unify both bioethanol/biodiesel production processes.
Hence, it only makes sense to consider the set of all transitively closed network hypotheses.
As for hypothesis 2, Leader closing behavior positively predicted employee exploitation behavior above and beyond the control variables (β = .26, P < .01).01
The renewal condition is then a natural hypothesis for the closing event, as the final state given by the asymptotic structure is well defined, but there's no way to know the exact time evolution that brought the system dynamics towards that particular asymptotic, stationary state.
However, the RMSEA = 0.065, with 90 % CI = (0.056, 0.074), and pclose = 0.003, suggests reasonable fit; the close-fit hypothesis was rejected (i.e., pclose < 0.05), but the poor-fit hypothesis was rejected (i.e., upper bound <0.10).
The RMSEA = 0.068, with 90 % CI = (0.059, 0.077), and pclose = 0.001, also suggests reasonable fit, although the close-fit hypothesis was rejected (i.e., pclose < 0.05), but the poor-fit hypothesis was also rejected (i.e., upper bound of the 90 % CI < 0.10).
