$I$-completeness in function spaces

In: Tatra Mountains Mathematical Publications, vol. 74, no. 2

Amar Kumar Banerjee - Apurba Banerjee

Details:

Year, pages: 2019, 35 - 46

Keywords:

ideal, filter, uniform space, $I$-Cauchy condition, $I$-convergence, ideal completeness.

Article type: mathematics

Document type: Scientific article *.pdf

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

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About article:

In this paper, we have studied the idea of ideal completeness of function spaces $Y^X$ 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 $Y^X$ 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.

How to cite:

ISO 690:

Banerjee, A., Banerjee, A. 2019. $I$-completeness in function spaces. In Tatra Mountains Mathematical Publications, vol. 74, no.2, pp. 35-46. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0017

APA:

Banerjee, A., Banerjee, A. (2019). $I$-completeness in function spaces. Tatra Mountains Mathematical Publications, 74(2), 35-46. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0017

About edition:

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

Published: 25. 10. 2019

Rights:

Licensed under the Creative Commons Attribution-NC-ND4.0 International Public License.