In this paper, we introduce the notion of almost pretopological vector spaces and present some examples of almost pretopological vector spaces. Almost pretopological vector spaces are defined by using regular open sets and pre-open sets. The relationships of almost pretopological vector spaces with certain other types of spaces are provided. Along with some useful results, it is proved that in almost pretopological vector spaces, translation and scalar multiple of a regular open (resp. regular closed) set are pre-open (resp. pre-closed).
References
[1]
Kolmogroff, A. (1934) Zur Normierbarkeit eines topologischen linearen Raumes. Studia Mathematica, 5, 29-33. https://doi.org/10.4064/sm-5-1-29-33
[2]
Khan, M.D., Azam, S. and Bosan, M.S. (2015) S-Topological Vector Spaces. Journal of Linear and Topological Algebra, 4, 153-158.
[3]
Khan, M. and Iqbal, M.A. (2016) On Irresolute Topological Vector Spaces. Advances in Pure Mathematics, 6, 105-112. https://doi.org/10.4236/apm.2016.62009
[4]
Ibrahim, H.Z. (2017) α-Topological Vector Spaces. Science Journal of University of Zakho, 5, 107-111. https://doi.org/10.25271/2017.5.1.310
[5]
Mashhour, A.S., Abd El-Monsef, M.E. and El-Deeb, S.N. (1982) On Precontinuous and Weak Precontinuous Mappings. Proceedings of the Mathematical and Physical Society of Egypt, 53, 47-53.
[6]
Levine, N. (1963) Semi-Open Sets and Semi-Continuity in Topological Spaces. American Mathematical Monthly, 70, 36-41. https://doi.org/10.1080/00029890.1963.11990039
[7]
Velicko, N.V. (1968) H-Closed Topological Spaces. American Mathematical Society Translations, 78, 103-118. https://doi.org/10.1090/trans2/078/05
[8]
Nasef, A.A. and Noiri, T. (1997) Some Weak Forms of Almost Continuity. Acta Mathematica Hungarica, 74, 211-219. https://doi.org/10.1023/A:1006507816942
