Amar Kumar Banerjee, Apurba Banerjee
Published 2017-04-18Version 1
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.
Spaces not distinguishing ideal pointwise and $σ$-uniform convergence
Uniform boundedness in function spaces
Selection principles in function spaces with the compact-open topology
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