This result is used to obtain a spectral characterization of the norm-closure of the class HC(H) of all hypercyclic operators acting on H, as well as a formula for the distance from a given operator to HC(H).
℘(V) does exist and is equal to V. The ordinals are defined by a non-positive condition, and do not make up a set, but it is interesting to note that the closure CL(On) of the class On of ordinals is equal to On ∪ {CL(On)}; the closure has itself as its only unexpected element.
We can also consider the closure and interior of the class U in a Hilbert space in the future.
The closure of all classes of the same grade mitigates the spread almost as much as closing the whole school.
While the closure of one class yields a smaller mitigation effect than the closure of the whole school, the closure of the corresponding grade (two classes) leads to a reduction of large outbreak probability and a reduction of epidemic size that are similar to those obtained by closing the entire school.
A slice distance for the class of weak abelian Lp-bundles in 3 dimensions was introduced in [20], where it was used to prove the closure of such class of bundles for the weak Lp-convergence.
the class is closed for a fixed duration ("targeted class closure" strategy); the class and the other class of the same grade are both closed for a fixed duration ("targeted grade closure" strategy); the entire school is closed for a fixed duration ("whole school closure" strategy).
one random class, different from the one in which symptomatic individuals are detected, is closed ("random class closure" strategy) the class and a randomly chosen one in a different grade are closed ("mixed class closure" strategy).
Moreover, while we have established the effectiveness of the class closure measures in reducing the spread within the school population, the effect of these measures on the spread in the rest of the population is not modelled nor quantified.
The recommended strategies were usually proportionate, with, for example, closure of a class if more than a certain number of children were absent in the class and closure of the school if more than a certain number of classes were affected.
