Homeomorphism between the underlying function space and the subspace of the function space

  • Edward Njuguna Muturi Egerton University

Abstract

The set of continuous functions from topological space \(Y\) to topological space \(Z\) endowed with topology \(\tau\) forms the function space \(C_\tau(Y,Z)\). For \(A\subset Y\), the set \(C(A,Z)\) of continuous functions from the space \(A\) to the space \(Z\) forms the underlying function space \(C_\zeta(A,Z)\) with the induced topology  \(\zeta\). Topology \(\tau\) and the induced topology \(\zeta\) satisfies properties of splitting or admissibility and  \(R_{A\subset Y}\)-splitting or \(R_{A\subset Y}\)-admissible properties respectively. In this paper we show that the  underlying function space \(C_\zeta(A,Z)\) is topologically equivalent to the subspace \(C_{\varrho}(U_\circ), (V_\circ)\) of the function space \(C_\tau(Y,Z)\).

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Published
2014-01-13
How to Cite
Muturi, E. N. (2014). Homeomorphism between the underlying function space and the subspace of the function space. Journal of Advanced Studies in Topology, 5(1), 57-60. https://doi.org/10.20454/jast.2014.724
Section
Original Articles