I-Completeness in Function Spaces

Amar Kumar Banerjee; Apurba Banerjee

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arXiv · 1704.05279

I-Completeness in Function Spaces

Amar Kumar Banerjee·Apurba Banerjee

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Abstract

In this paper we have studied the idea of ideal completeness of function spaces Y to the power X with respect to pointwise uniformity and uniformity of uniform convergence. Further involving topological structure on X we have obtained relationships between the uniformity of uniform convergence on compacta on Y to the power X and uniformity of uniform convergence on Y to the power X in terms of I-Cauchy condition and I-convergence of a net. Also using the notion of a k-space we have given a sufficient condition for C(X,Y) to be ideal complete with respect to the uniformity of uniform convergence on compacta.

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BibTeX RIS

Amar Kumar Banerjee, Apurba Banerjee. 2017-04-18. I-Completeness in Function Spaces. https://arxiv.org/abs/1704.05279

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