登入選單
返回Google圖書搜尋
Topological Algebras
出版Elsevier, 2011-10-10
主題Mathematics / Geometry / AlgebraicMathematics / Topology
ISBN00808713569780080871356
URLhttp://books.google.com.hk/books?id=WBwYpZapEPAC&hl=&source=gbs_api
EBookSAMPLE
註釋This book discusses general topological algebras; space C(T,F) of continuous functions mapping T into F as an algebra only (with pointwise operations); and C(T,F) endowed with compact-open topology as a topological algebra C(T,F,c). It characterizes the maximal ideals and homomorphisms closed maximal ideals and continuous homomorphisms of topological algebras in general and C(T,F,c) in particular. A considerable inroad is made into the properties of C(T,F,c) as a topological vector space. Many of the results about C(T,F,c) serve to illustrate and motivate results about general topological algebras. Attention is restricted to the algebra C(T,R) of real-valued continuous functions and to the pursuit of the maximal ideals and real-valued homomorphisms of such algebras. The chapter presents the correlation of algebraic properties of C(T,F) with purely topological properties of T. The Stone–Čech compactification and the Wallman compactification play an important role in characterizing the maximal ideals of certain topological algebras.