Muturi, N.E. (2014) Homeomorphism between the Underlying Function Space and the Subspace of the Function Space. Journal of Advanced Studies in Topology, 1, 57-60.

has been cited by the following article:

• TITLE: Heredity of Lower Separation Axioms on Function Spaces

  AUTHORS: Njuguna E. Muturi

  KEYWORDS: Function Space; Underlying Function Space; Hereditary Properties

  JOURNAL NAME: Advances in Pure Mathematics, Vol.4 No.3, March 28, 2014

  ABSTRACT: 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.