Search results for "Topological space"
showing 4 items of 54 documents
Topological linguistics and the study of linguistic variation
1994
Publisher Summary This chapter focuses on topological linguistics and the study of linguistic variation. It discusses the problem of linguistic variation. A topological model has been developed for internal linguistics, starting from the epistemological problem that all linguists must deal with. A topological space could be conceived of as a set of elements where some elements limit the others and are said to be open-sets, and the former and the latter together constitute the closed-sets. Linguistics, when approaching its object of study, is faced with a very similar situation: a language is a set of elements—from utterances to minimal phonic items—where each is described by other surroundi…
Categorical foundations of variety-based topology and topological systems
2012
The paper considers a new approach to fuzzy topology based on the concept of variety and developed in the framework of topological theories resembling those of Rodabaugh. As a result, a categorical generalization of the notion of topological system of Vickers is obtained, and its theory unfolded, which clarifies the relations between algebra and topology. We also justify the use of semi-quantales as the basic underlying structure for doing lattice-valued topology as well as provide a categorical framework incorporating the theory of bitopological spaces.
Composite variety-based topological theories
2012
Motivated by the recent result of Rodabaugh on categorical redundancy of lattice-valued bitopology, the paper considers another viewpoint on the topic, based on the notion of composite variety-based topological theory. The new concept, apart from providing a variable-basis generalization of bitopology, incorporates the most important approaches to topology currently developed in the fuzzy community, bringing forward their categorically algebraic properties, which are cleared from point-set lattice-theoretic dependencies. Dwelling on different ways of interaction between composite topology and topology, e.g., embedding the former into the latter as a full bicoreflective subcategory, we final…
Generalized fuzzy topology versus non-commutative topology
2011
The paper introduces a modification of the notions of generalized fuzzy topological space of Demirci and quantal space of Mulvey and Pelletier, suitable to explore interrelations between point-set lattice-theoretic topology and non-commutative topology developed in the framework of C^*-algebras or (more recently) of quantales. As a consequence of the new approach, a generalization of the concept of topological system of Vickers arises. Moreover, the currently dominating variable-basis topological setting in the fuzzy community, due to Rodabaugh, appears to be ''fixed-basis''.