<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we have studied the idea of ideal completeness of function spaces <italic>YX</italic> with respect to pointwise uniformity and uniformity of uniform convergence. Further, involving topological structure on <italic>X</italic>,wehaveobtained relationships between the uniformity of uniform convergence on compacta on <italic>YX</italic> and uniformity of uniform convergence on <italic>Y X</italic> in terms of <italic>I</italic>-Cauchy condition and <italic>I</italic>-convergence of a net. Also, using the notion of a <italic>k</italic>-space, we have given a sufficient condition for <italic>C</italic>(<italic>X, Y</italic>) to be ideal complete with respect to the uniformity of uniform convergence on compacta.</abstract>

In this paper, we have studied the idea of ideal completeness of function spaces YX with respect to pointwise uniformity and uniformity of uniform convergence. Further, involving topological structure on X,wehaveobtained relationships between the uniformity of uniform convergence on compacta on YX and uniformity of uniform convergence on Y 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.

<italic>I</italic>-Completeness in Function Spaces

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":{"italic":"I","content":"-Completeness in Function Spaces"}}

In this paper, we have studied the idea of ideal completeness of function spaces YX with respect to pointwise uniformity and uniformity of uniform convergence....

I-Completeness in Function Spaces

Published Online: Nov 15, 2019

Page range: 35 - 46

Received: May 15, 2017

DOI: https://doi.org/10.2478/tmmp-2019-0017

Keywords
ideal, filter, uniform space, -Cauchy condition, -convergence, ideal completeness

© 2019 Amar Kumar Banerjee et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

I-Completeness in Function Spaces

Published Online: Nov 15, 2019

Page range: 35 - 46

Received: May 15, 2017

DOI: https://doi.org/10.2478/tmmp-2019-0017

Keywordsideal, filter, uniform space, -Cauchy condition, -convergence, ideal completeness

© 2019 Amar Kumar Banerjee et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
ideal, filter, uniform space, -Cauchy condition, -convergence, ideal completeness