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As a result, the set Uy(t) is also relatively compact set in X for t [member of] [0, [infinity]).

Existence and Attractivity for Fractional Evolution Equations

Recall from [3] that an operator T : E [right arrow] X is said to be b-AM-compact if it carries b-order bounded set of E (i.e., order bounded in E") into norm relatively compact set of X.

Note that every relatively compact set is limited but the converse is not true in general.

Some results on AM-compact operators

Consider [mathematical expression not reproducible] the subfamily of [W.sup.n,1]([[0, T].sup.N]) consisting of relatively compact sets in the topology [[tau].sup.[omega]] and [mathematical expression not reproducible] the family of all nonempty and bounded subsets (innorm) of [W.sup.n,1]([[0, T].sup.N]).

A Family of Measures of Noncompactness in the Locally Sobolev Spaces and Its Applications to Some Nonlinear Volterra Integrodifferential Equations

Therefore, letting [epsilon] [right arrow] 0, we see that, there are relatively compact sets arbitrarily close to the set {[phi](t): [phi] [member of] B([B.sub.l])[parallel].

Solvability of impulsive neutral integrodifferential inclusions with nonlocal initial conditions via fractional operators

Because a well-known result states that in complete metric spaces, relatively compact sets coincide with pre-compact sets, it is sufficient to show that for any [epsilon] > 0, the set of values of the function can be embedded in a finite number of spheres of radius [epsilon].

Almost periodic functions with values in p-frechet spaces, 0 < p < 1