Then since X' is a separable Banach space, the set of all smooth points of X' is a

dense subset of X' and as before the set of all smooth points of X' contained in V is dense in V.

e) The empty set is the only nowhere

dense subset of X.

A) {A(t) : t G J} be a family of linear (not necessarily bounded) operators, A(t) : D(A) [subset] E [right arrow] E, D(A) not depending on t and

dense subset of E and T : [DELTA] = {(t, s) : 0 [less than or equal to] s [less than or equal to] t [less than or equal to] b} [right arrow] L(E) be the evolution operator generated by the family {A(t) : t [member of] J}.

Finally, after the 6-day descent to sea level, we observed a dramatic decrease in the number of RBCs in the low and middle density subsets and a corresponding increase (more than 3 times the control levels) of cells in the

dense subset.

In such a case all claims hold for some open and

dense subset of X rather than for X.

being an open

dense subset of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.

Since [phi] is irreducible, Mathematical Expression Omitted] ranges over a linearly

dense subset of [H.

If the preordering [less than or equal to] is taken as a complete preference relation on the commodity magnitude set c and if c has a countably

dense subset, then (c, [less than or equal to]) is an ordinal structure and the representation q of c in [r.

Let D [subset or equal to] S be a

dense subset and fix [x.

As the ideal of all finite-rank operators in B(H) is a

dense subset of B(H) in the weak operator topology, we obtain that [psi][(T).

t[greater than or equal to]0] is chaotic or stable, or has got a

dense subset of its periodic points, then the system [([[?

Since [Mathematical Expression Omitted] is a

dense subset of [Mathematical Expression Omitted], it follows that u(f) = fu(1) for any [Mathematical Expression Omitted] and whence the ideal I([Omega]) is principal in O([Omega]), generated by u(1).