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Heredity of Lower Separation Axioms on Function Spaces

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DOI: 10.4236/apm.2014.43014    2,983 Downloads   4,372 Views  

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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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