A note on P-I-convergence

• Carlos Granados Corporación Universitaria Latinoamericana

Keywords: pre-I-convergencia, funciones pre-I-irresolutas, funciones que preservan pre-I-convergencia, pre-I-secuencialmente abierto, espacios pre-I-secuenciales, funciones de pre-I-cobertura, espacios pre-I-Fréchet-Urysohn

Abstract

In this article, we use the notions of pre-open and pre-I-open sets to introduce the idea of pre-I-convergence which we will denoted by P -I-convergence, we also show some of its properties. Besides, some basic properties of pre-I-Fréchet-Urysohn space is shown. Moreover, notions related to pre-I-sequential and pre-I-sequentially are proved. Furthermore, we show some relations of pre-I-irresolute functions between preserving pre-I-convergence functions and pre-I-covering functions.

References

Boone, J. and Siwiec, F., Sequentially quotient mappings, Czechoslov. Math. J., 26(2018), 174–182.

Dontchev, J., Idealization of Ganster-Reily decomposition theorem, http://arxiv.org/abs/Math.GN/9901017, 5 Jan. 1999.

Franklin, S., Spaces in which sequences suffice, Fund. Math., 57(1965), 107–115.

Kuratowski, K., Topologie, Monogrfie Matematyczne tom 3, PWN-ploish Scientific Publishers, Warszawa, 1933.

Lin, S. and Yun, Z., Generalized metric spaces and mapping, Atlantis Studies in Mathematics, 6(2016).

Mahhour, A, Hassanein, I. and El-Deeb, S., A note on semi-continuity and precontinuity, Indian J. Pure Appl. Math., 13(10)(1982), 1119–1123.

Zhou, X. and Lin, S., On topological spaces defined by I-convergence, Bulletin of the Iranian Mathematical Society, 2019.