# dense subset

## dense subset

[¦dens ′səb‚set]
(mathematics)
A subset of a topological space whose closure is the entire space.
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Definition 4.1 (Asplund F-space/G-space/GD-space) An Asplund F-space is a Banach space with the following property: If is a continuous convex function defined in open and convex subset U [subset] X, then F-differentiable in a dense subset [G.sub.[delta]] of U.
Transitivity usually implies the existence of dense orbit, if [there exists][x.sub.0] [member of] X such that Orb([x.sub.0]) is a dense subset of X.
Step 2: Prove that the sequence converges on a dense subset.
(6) Let X be an almost convex dense subset of an admissible subset Y of a t.v.s.
Choose a countable dense subset T = {[t.sub.1], [t.sub.2] ,...} in the domain [0,1], and put, where [R.sup.{1}.sub.t] (s) is reproducing kernel of [W.sup.1.sub.2]1[0,1].
The spaces [W.sup.F](M, p) and [W.sup.F.sub.0](M,p) are nowhere dense subset of [W.sup.F](M, p).
(e) The empty set is the only nowhere dense subset of X.
Let D := [{[g.sub.n]}.sub.n] = [{([g.sub.n](1), [g.sub.n](2), ...)}.sub.n] denote a countable dense subset of [omega] satisfying [g.sub.n](j) = 0 if and only if j > n.
(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.
Property 2 [X.sub.p]([F.sup.t]) is a dense subset of [g.sub.t]([X.sub.p](F)).

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