Heredity of Lower Separation Axioms on Function Spaces

作     者：Njuguna E. Muturi 

作者机构：Department of Mathematics Egerton University Egerton Kenya 

出 版 物：《Advances in Pure Mathematics》 (理论数学进展（英文）)

年 卷 期：2014年第4卷第3期

页      面：89-92页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Function Space Underlying Function Space Hereditary Properties 

摘      要：The set of continuous functions from topological space Y to topological space Z endowed with a topology forms the function space. For A subset of Y, the set of continuous functions from the space A to the space Z forms the underlying function space with an induced topology. The function space has properties of topological space dependent on the properties of the space Z, such as the T0, T1, T2 and T3 separation axioms. In this paper, we show that the underlying function space inherits the T0, T1, T2 and T3 separation axioms from the function space, and that these separation axioms are hereditary on function spaces.