α-Topological Vector Spaces
DOI:
https://doi.org/10.25271/2017.5.1.310Keywords:
α-Topological vector space, α-open set, α-irresolute mapping, left (right) translation, α-homeomorphismAbstract
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).
References
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).
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY-NC-SA 4.0] that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work, with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online.