Sentence examples for is closed since from inspiring English sources

Assume this not to be the case, so that there is k ∈ Z + such that ⋃ n = 0 ∞ A 0 n = ( ⋃ n = 0 k − 1 A 0 n ) ∪ ( ⋃ n = k ∞ A 0 n ) is closed with ⋃ n = k ∞ A 0 n not being closed and such that ⋃ n = 0 k A 0 n is closed, since it is the union of a finite number of closed sets.

Moreover, is closed, since is closed on.

By Proposition 2.1 in [17], the set N is closed, since its elements are (C^{1}).

A is closed since ϕ is lower semi-continuous by Proposition 2.1 and so it is compact.

This idea is intimately related to the thesis that knowledge is closed, since, according to some theorists, knowing p entails justifiably believing p. If knowledge entails justification, closure failure of the latter might lead to closure failure of the former.

Now we show that y is the fixed point of g and T. Assume that TX is closed, since { y 2 n = T x 2 n + 1 } is a sequence in TX converging to y, we have y ∈ T X.

She says she's heard that the Mall has been closed since before noon anyway.

But the gap is closing: Since the spring, Yahoo! has been doing gangbuster business.

The lab, which has been closed since Monday, will remain closed tomorrow and possibly Friday.

The restaurant has been closed since 2008.

The ride has been closed since Thursday.