Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2016, 4(2), 35-38
DOI: 10.12691/tjant-4-2-2
Open AccessArticle

On Irresolute Topological Vector Spaces-II

Muhammad Asad Iqbal1, Muhammad Maroof Gohar2 and Moiz ud Din Khan1,

1Mathematics COMSATS Institute of Information Technology, Park Road, Chak Shahzad, 45550 Islamabad, PAKISTAN

2Mathematics, G.C. University, Lahore, Pakistan

Pub. Date: June 25, 2016

Cite this paper:
Muhammad Asad Iqbal, Muhammad Maroof Gohar and Moiz ud Din Khan. On Irresolute Topological Vector Spaces-II. Turkish Journal of Analysis and Number Theory. 2016; 4(2):35-38. doi: 10.12691/tjant-4-2-2

Abstract

In this paper, we continue the study of Irresolute topological vector spaces. Notions of convex, bounded and balanced set are introduced and studied for Irresolute topological vector spaces. Along with other results, it is proved that: 1. Irresolute topological vector spaces are semi-Hausdorff spaces. 2. Every Irresolute topological vector space is semi-regular space. 3. In Irresolute topological vector spaces, as well as is convex if is convex. 4. In Irresolute topological vector spaces, is bouned if is bounded. 5. In Irresolute topological vector spaces, is balanced if is balanced and 6. In Irresolute topological vector spaces, every semi compact set is bounded.

Keywords:
topological vector space irresolute topological vector space irresolute mapping semi open set

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References:

[1]  Moiz ud Din Khan, Muhammad Asad Iqbal, On Irresolute topological vector space, Adv. Pure Math. 6(2016), 105-112.
 
[2]  Muhammad Saddique Bosan, s-Topological groups, 2015, (Ph.D Thesis).
 
[3]  N. Levine, Semi-Open Sets and Semi-Continuity in Topological Spaces, Amer. math. month., 70(1) (1963), 37-41.
 
[4]  Crossley, S.G. and Hildebrand, S.K. Semi-Topological Properties. Fundamental Mathematicae, 74(1972), 233-254.
 
[5]  Crossley, S.G. and Hildebrand, S.K. Semi-Closure, Texas J. Sci., 22(1971), 99-112.