Moreover, there exists a nonempty, compact, and closed subset and such that.
(IV By the assumption (v), there exists a nonempty, compact, and closed subset and such that, for all, we have.
In contrast, in the GTP bound state, TG2 exists in a compact and closed structure that decreases the accessibility of the active site [8], [9].
Thus, a compact and closed conformation opens up and exposes a large hydrophobic area which is capable of recognizing and binding potential targets (Malashkevich et al., 2008).
We have included in the discussion a reference to Focke et al. (J. Neuroscience 2011), who have suggested that the apo form would be as compact and closed as the fully bound form.
But with work, humility and seriousness, we'll get there"; Pablo Zabaleta says their strengths are spoiling, staying "compact and tight", "closing down" and feeding on negativity.
For each, is compact since is compact and is closed.
If is compact and is closed, then there exists and such that for all and.
By Lemma 2.3, there exists such that since is compact and hence closed.
(see [9]) If (the closure of ) is compact and is closed, then is u.s.c.s.c
