Some Properties Of Neat Topological Monoids

A topological semigroup is a semigroup with topological structure,which makes the semigroup operation continuous.The fusion of topological structure and semigroup structure of topological semigroups has produced a lot of meaningful research results.In this thesis,we introduce a new class of topological monoids,which we call neat topological monoids,by constructing the neighborhood basis of the identity element.We discuss some basic structures and properties of the neat topological monoids as well as the quotient and(?)ech-Stone compactification of the neat topological monoids.Thus we proved the following results:1.The way of a monoids being topologically transformed into a neat topological monoid,and some examples of constructing neat topological monoids are given;2.Some substructure properties of neat topological monoids are given;3.Some separation conclusions of neat topological monoids are given;4.Congruences R and equivalence classes x R on monoids are given;5.The properties of quotient mappings and homomorphism theorems of neat topological monoids are given;6.The Cartesian product of quotient of neat topological monoids and related properties are given;7.The way to transform the(?)ech-Stone compact space ? S of a neat topological monoid into a right topological semigroup is given;8.Using the product structure of ultrafilters to describe the product in ?S is given.