On \(\alpha\)-topological vector space
Downloads
DOI:
https://doi.org/10.26637/MJM0803/0067Abstract
The purpose of this article is to continue the study of \(\alpha\)-topological vector space in the spirit of \(\alpha\)-open set, \(\alpha\)-closed set, \(\alpha\)-continuous mapping from the previous paper by O. Njastad [10], A.S. Mashhour [9], S.N. Maheshwari and S.S. Thakur [7,8]. Several properties of \(\alpha\)-topological vector space are obtained. There are many more properties of the type translation, dilation and deep structure of the space are described in detail.
Keywords:
\(\alpha\)-open sets , \(\alpha\)-closed sets , \(\alpha\)-topological vector spaceMathematics Subject Classification:
Mathematics- Pages: 1126-1131
- Date Published: 01-07-2020
- Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
T. Al-Hawary and A. Al-Nayef, On IrresoluteTopological Vector Spaces, Math. Sci. Res. Hot-Line, 5(2001), 49-53.
D.H. Hyers, Pseuso-normed linear spaces and abelian groups, Duke Math. J., 5(1939), 628-634.
M.D. Khan, S. Azam and M. S. Bosan, s-Topological Vector Space, Journal of Linear and Topological Algebra, $04(02)(2015), 153-158$.
M.D. Khan and M.A. Iqbal, On Irresolute Topological Vector Spaces, Adv. Pure Math., 6(2016), 105-112.
M.A. Iqbal, M.M. Gohar and M.D. Khan, On Irresolute Topological Vector Spaces-II, Turkish Journal of Analysis and Number Theory, 4(2)(2016), 35-38.
A. Kolmogroff, ZurNormierbarkeiteinestopologischenlinearenRaumes, Studia Math., 5(1934), 29-33.
S.N. Maheshwari and S.S. Thakur, On $alpha$-compact spaces, Bull. Inst. Math. Acad. Sinica. 13(1985), 341-347.
$[8]$ S.N. Maheswari and S.S. Thakur, $alpha$-irresolute mappings, Tamkang Jour. Math., 11(1980), 209-214.
A.S. Mashhour, I.A. Hasanein, S.N. El-Deeb, $alpha-$ continuous and $alpha$-open mappings, Acta Math. Hungar., 41(1983), 213-218.
O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), 961-970.
N. Rajesh, Thanjavur and V. Vijayabharathi, On strongly preirresolute topological vector space, Mathematica Bohemica, 138(2013), 37-42.
M. Ram, Correction to the Paper: On Irresolute Topological Vector Space-II, Turkish Journal of Analysis and Number Theory, 6(4)(2018), 124-124.
M. Ram, S. Sharma, Corrigendum to: On Irresolute Topological Vector Spaces, New Trends Math. Sci., 6(4)(2018), $40-44$
M. Ram, S. Sharma, S. Billawria and A. Hussain, On Almost s-Topological Vector Spaces, Jour. Adv. Stud. Topol., 9(2)(2018), 139-146.
${ }^{[15]}$ H. H. Schaefer, Topological Vector Spaces, SpringerVerlag New York Heidelberg Berlin, 1971.
S. Sharma, M. Ram and S. Billawria, On Almost Pretopological Vector Spaces, Open Access Library Journal, 5(2018), 01-10.
S. Sharma and M. Ram, On $beta$-Topological Vector Spaces, Journal of Linear and Topological Algebra, 8(01)(2019), 63-70.
J. V. Wehausen, Transformations in linear topological spaces, Duke Math. J., 4(1938), 157-169.
- NA
Similar Articles
- B. M. Uzzal Afsan, On fuzzy inverse systems of fuzzy topological spaces , Malaya Journal of Matematik: Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.