Categories of ordered sets
The problem whether every topological space has a compactification such that every continuous mapping from into a compact space has a continuous extension from into is answered in the negative. For some spaces such compactifications exist.
In the present paper, fuzzy order relations on a real vector space are characterized by fuzzy cones. It is well-known that there is one-to-one correspondence between order relations, that a real vector space with the order relation is an ordered vector space, and pointed convex cones. We show that there is one-to-one correspondence between fuzzy order relations with some properties, which are fuzzification of the order relations, and fuzzy pointed convex cones, which are fuzzification of the pointed...
We give Lambek-Carlitz type characterization for completely multiplicative reduced incidence functions in Möbius categories of full binomial type. The -analog of the Lambek-Carlitz type characterization of exponential series is also established.
In the category of symmetric graphs there are exactly five closed tensor products. If we omit the requirement of units, we obtain twelve more.