Let Y be a proximinal subspace of finite codimension of c0. We show that Y is proximinal in ∞ and the metric projection from ∞ onto Y is Hausdorff metric continuous. In particular, this implies that the metric projection from ∞ onto Y is both lower Hausdorff semi-continuous and upper Hausdorff semi-continuous.

In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice. We firstly illustrate the concepts of strict left (right)-conjunctive left (right) semi-uninorms by means of some examples. Then we give out the formulas for calculating the upper and lower approximation strict left (right)-conjunctive left (right) semi-uninorms of a binary operation.

In this paper we prove a single exponential upper bound on the number of possible homotopy types of the fibres of a Pfaffian map in terms of the format of its graph. In particular, we show that if a semi-algebraic set S ⊂ Rm+n, where R is a real closed field, is defined by a Boolean formula with s polynomials of degree less than d, and π : Rm+n → Rn is the projection on a subspace, then the num...

In this paper, we present the boundedness of solution set of tensor complementarity problem defined by a strictly semi-positive tensor. For strictly semi-positive tensor, we prove that all H+(Z+)-eigenvalues of each principal sub-tensor are positive. We define two new constants associated with H+(Z+)-eigenvalues of a strictly semi-positive tensor. With the help of these two constants, we establ...

We show that any compact semi-algebraic subset of mixed action profiles on a fixed player set can be represented as the projection of the set of equilibria of a game in which additional binary players have been added. Even stronger, we show that any semi-algebraic continuous function, or even any semi-algebraic upper-semicontinuous correspondence with nonempty values, from a bounded semi-algebr...

In conclusion, I may point out that Theorem II may be generalized by a weakening of the hypothesis (d) . (1) In the first place, continuity of [a, g] f with respect to the pair of variables a, /3 may be replaced by upper semi-continuity . This generalization requires no change in the proof . (2) This continuity (or upper semi-continuity) with respect to (a, /3) is used only to show that the set...

The radiation pattern of a line source is calculated for the case where the source is lying on the top or the bottom surface of a lossless dielectric substrate that is mounted on the top of a semi-infinite dielectric medium. It is found that in both cases the pattern along interfaces has a null; that the pattern in the upper semi-infinite medium has a single lobe; and that the pattern in the lo...

In this paper, we introduce a framework which can be used for establishing an upper bound on message latency, suitable for construction of Internet-based partially synchronous overlay networks. We propose two network filters for estimating the network states and implement them along with the five other network estimators proposed by other researchers. We monitor various Internet paths by measur...

Recently Sénizergues showed decidability of the equivalence problem for deterministic pushown automata. The proof of decidability is two semi-decision procedures that do not give a complexity upper bound for the problem. Here we show that there is a simpler deterministic decision procedure that has a primitive recursive upper bound.