α-Topological Vector Spaces

  • Hariwan Z. Ibrahim University of Zakho
DOI: https://doi.org/10.25271/2017.5.1.310
Keywords: α-Topological vector space, α-open set, α-irresolute mapping, left (right) translation, α-homeomorphism

Abstract

The main objective of this paper is to present the study of α-topological vector spaces. α-topological vector spaces are defined by using α-open sets and α-irresolute mappings. Notions of convex, balanced and bounded set are introduced and studied for α-topological vector spaces. Along with other results, it is proved that every α-open subspace of an α-topological vector space is an α-topological vector space. A homomorphism between α-topological vector spaces is α-irresolute if it is α-irresolute at the identity element. In α-topological vector spaces, the scalar multiple of α-compact set is α-compact and αCl(C) as well as αInt(C) is convex if C is convex. And also, in α-topological vector spaces, αCl(E) is balanced (resp. bounded) if E is balanced (resp. bounded), but αInt(E) is balanced if E is balanced and 0 ∈ αInt(E).

Author Biography

Hariwan Z. Ibrahim, University of Zakho

Dept. of Mathematics, Faculty of Science, University of Zakho, Zakho, Kurdistan Region, Iraq

References

A. Grothendieck, Topological vector spaces, New York: Gordon and Breach Science Publishers, (1973).
D. Jangkovic , I. J. Reilly and M. K. Vamanamurthy , On strongly compact topolog- ical spaces, Question and answer in General Topology, 6 (1) (1988), 29-40.
N. Levine. Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1) (1963), 36-41.
S. N. Maheshwari and S. S. Thakur, On α-irresolute mappings, Tamkang J. Math. 11 (2) (1980), 209-214.
O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961-970.
M. Khan and B. Ahmad, On P-regular spaces, Math. Today, XIII, (1995), 51-56.
A. P. Robertson, W. J. Robertson, Topological vector spaces, Cambridge Tracts in Mathematics. 53. Cambridge University Press, (1964).
Published
2017-03-30
How to Cite
Ibrahim, H. (2017). α-Topological Vector Spaces. Science Journal of University of Zakho, 5(1), 107-111. https://doi.org/10.25271/2017.5.1.310
Issue
Vol 5 No 1 (2017): March, 2017
Section
Science Journal of University of Zakho

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