Some problems in set topology relating group of homeomorphisms and order

In this thesis we investigate some problems in set theoretical topology related to the concepts of the group of homeomorphisms and order. Many problems considered are directly or indirectly related to the concept of the group of homeomorphisms of a topological space onto itself. Order theoretic methods are used extensively. Chapter-l deals with the group of homeomorphisms. This concept has been investigated by several authors for many years from different angles. It was observed that nonhomeomorphic topological spaces can have isomorphic groups of homeomorphisms. Many problems relating the topological properties of a space and the algebraic properties of its group of homeomorphisms were investigated. The group of isomorphisms of several algebraic, geometric, order theoretic and topological structures had also been investigated. A related concept of the semigroup of continuous functions of a topological space also received attention

Some Lattice Problems In Fuzzy Set Theory And Fuzzy Topology

It is believed that every fuzzy generalization should be formulated in such a way that it contain the ordinary set theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9] with an arbitrary complete and distributive lattice as the membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy topologies on a set. It is proved that in general, the lattice of fuzzy topologies is not complemented. Complements of some fuzzy topologies are found out. It is observed that (L,X) is not uniquely complemented. However, a complete analysis of the problem of complementation in the lattice of fuzzy topologies is yet to be found out

Author Identification in Malayalam using n-grams

Author identification is the problem of identifying the author of an anonymous text or text whose authorship is in doubt from a given set of authors. The works by different authors are strongly distinguished by quantifiable features of the text. This paper deals with the attempts made on identifying the most likely author of a text in Malayalam from a list of authors. Malayalam is a Dravidian language with agglutinative nature and not much successful tools have been developed to extract syntactic & semantic features of texts in this language. We have done a detailed study on the various stylometric features that can be used to form an authors profile and have found that the frequencies of word collocations can be used to clearly distinguish an author in a highly inflectious language such as Malayalam. In our work we try to extract the word level and character level features present in the text for characterizing the style of an author. Our first step was towards creating a profile for each of the candidate authors whose texts were available with us, first from word n-gram frequencies and then by using variable length character n-gram frequencies. Profiles of the set of authors under consideration thus formed, was then compared with the features extracted from anonymous text, to suggest the most likely author.