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 APM  Vol.4 No.3 , March 2014
Heredity of Lower Separation Axioms on Function Spaces
Njuguna E. Muturi*
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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.
Keywords: Function Space; Underlying Function Space; Hereditary Properties
Cite this paper: Muturi, N. (2014) Heredity of Lower Separation Axioms on Function Spaces. Advances in Pure Mathematics, 4, 89-92. doi: 10.4236/apm.2014.43014.
References

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[7]   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.

 
 
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