In this paper, we characterize stratifiable (or semi-stratifiable) spaces, and monotonically countably paracompact metacompact) spaces by expansions of locally upper bounded semi-continuous poset-valued maps. These extend earlier results for real-valued Locally functions.

In this paper, we study some of the properties of interval valued fuzzy generalized semi-preirresolute mappings.

Let G be a finite connected graph, and let ∆ be its universal covering tree. The edges of ∆ are directed and each geometric edge corresponds to two directed edges δ and δ. Let ∆ be the set of vertices and ∆ the set of directed edges of ∆. The boundary ∂∆ is the set of equivalence classes of infinite semi-geodesics in ∆, where two semi-geodesics are equivalent if they agree except on finitely ma...

The Nielsen number for n-valued multimaps, defined by Schirmer, has been calculated only for the circle. A concept of n-valued fiber map on the total space of a fibration is introduced. A formula for the Nielsen numbers of n-valued fiber maps of fibrations over the circle reduces the calculation to the computation of Nielsen numbers of single-valued maps. If the fibration is orientable, the pro...

We introduce the notion of a C *-valued weight between two C *-algebras as a generalization of an ordinary weight on a C *-algebra and as a C *-version of operator valued weights on von Neumann algebras. Also, some form of lower semi-continuity will be discussed together with an extension to the Multiplier algebra. A strong but useful condition for C *-valued weights, the so-called regularity, ...

This paper introduces singular mix-valued logical networks and singular mix-valued logical control networks. Via semi-tensor product, a singular mix-valued logical network can be converted to an algebraic form. On this basis, the normalization problem and solvability are discussed. Then, fixed points and cycles of singular mix-valued logical networks are also studied. Furthermore, the optimal c...