motivated by the recent study on categorical properties of latticevalued topology, the paper considers a generalization of the notion of topological system introduced by s. vickers, providing an algebraic and a coalgebraic category of the new structures. as a result, the nature of the category   topsys   of s. vickers gets clari ed, and a metatheorem is stated, claiming that (latticevalu...

Fundamental to amassing a lexicon of relational terms (i.e., verbs, prepositions) is the ability to abstract and categorize spatial relations such as a figure (e.g., boy) moving along a path (e.g., around the barn). Three studies examine how infants learn to categorize path over changes in manner, or how an action is performed (e.g., running vs. crawling). Experiment 1 (n = 60) finds that 10- t...

in this paper, we formalize the menger probabilistic normed space as a category in which its objects are the menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. so, we can easily apply the results of topological vector spaces...