Connectedness Of Finite Matroids And Mapping Of Poset Matroids

Matroids is an abstract and extension of the concepts of graph, matrix, vector correlation, etc., whick has broad applications in combinatorial optimization, integer programming, network flow and electricical fence theory. Based on the way of topology theory, partially ordered theory and category theory, this paper mainly discusses two aspects of matroids: connectedness of finite matroids and mapping of poset matroids. The concepts of connected matroids, connected components, PO mapping, open mapping, closed mapping and homeomorphism mapping are given, and make a systema tical research on their natures is maded, especially the natures of Ky Fan's (Fanji's) theorem in connected matroids and morphisms in poset matroids category are studied.The construction and main contents of this paper is as follows:In chapter 1 We maked a depiction for basic knowledge and basic conclusions of finite matroids, poset matroids and category which would be used in the following chapters.In chapter 2 In this chapter, the theory of matroids is studied with help of ways of topology, a new connectedness in finite matroids is defined, with open set, closed set on the concept of connectedness in finite matroids is discussed, including connected components and Ky Fan's (Fanji's) theorem, and it is pointed out to be relationship to the connected matroids that had defined.In chapter 3 In this chapter, firstly PO mapping, open mapping, closed mapping and homeomorphism mapping in the poset matroids are defined. Secondly relationships between those notions and an existing notion of mapping of poset matroids are discussed, and relationships to mappings are obtained, moreover, invariance in those mappings is given, finally, propertities in poset matroids of category are discussed, specific characterizations of mononmorphism, extrmal monomorphism, epimo-rphism, extrmal epimorphism and concrete structure of equalizer, coequalizer in poset matroids are given.