Abstract:
The set of continuous functions from topological space Y to topological space Z endowed with topology T forms the function space C<sub>T </sub>(Y;Z). For A ⊂Y , the set C(A;Z) of continuous functions from the space A to the space Z forms the underlying function space Cζ(A;Z) with the induced topology ζ. Topology T and the induced topology ζ satisfies properties of splitting or admissibility and R<sub> A⊂</sub>Y -splitting or R <sub>A⊂</sub>Y -admissible properties respectively. In this paper we show that the underlying function space Cζ(A;Z) is topologically equivalent to the subspace Cϱ(U∘ V∘) of the function space C<sub>T</sub>(Y;Z).
