We show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. Further we study the preservation of diagonal conditions, which characterize approach spaces. It is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...

A setoid is a set together with a constructive representation of an equivalencerelation on it. Here, we give category theoretic support to the notion. Wefirst define a category Setoid and prove it is cartesian closed with coproducts.We then enrich it in the cartesian closed category Equiv of sets and classicalequivalence relations, extend the above results, and prove that Setoid...

the application of laser in dentistry is considered as a favorable technique for patients due to its many advantages compare to other current methods. one of the main goals in pediatric dentistry is to provide the treatment as comfortable as possible without any risks for the care. laser is being used in different pediatric dental conditions including caries detection, caries removal and cavity...

Let D1, D2, D be non empty sets and let x be an element of [: [:D1, D2 :], D :]. Then x1,1 is an element of D1. Then x1,2 is an element of D2. Let D1, D2 be non empty sets and let x be an element of [:D1, D2 :]. Then x2 is an element of D2. Next we state the proposition (1) Let C, D be category structures. Suppose the category structure of C = the category structure of D. If C is category-like,...

In computational linguistics, a large body of work exists on distributed modeling lexical relations, focussing largely relations such as hypernymy (scientist -- person) that hold between two categories, expressed by common nouns. contrast, linguistics has paid little attention to entities denoted proper nouns (Marie Curie, Mumbai, ...). These have investigated in detail the Knowledge Representa...

we show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. further we study the preservation of diagonal conditions, which characterize approach spaces. it is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...