Article Versions
Export Article
Cite this article
  • Normal Style
  • MLA Style
  • APA Style
  • Chicago Style
Erratum
Open Access Peer-reviewed

Correction to the Paper “On Irresolute Topological Vector Spaces-II”

Madhu Ram
Turkish Journal of Analysis and Number Theory. 2018, 6(4), 124-124. DOI: 10.12691/tjant-6-4-4
Received October 05, 2018; Revised November 06, 2018; Accepted November 18, 2018

Abstract

In the published paper [1], Theorem 3.26, Theorem 3.27 and Theorem 3.30 are not correct. Here we give an authentic refutation of these theorems.

1. Refutation of [[1], Theorem 3.26, Theorem 3.27, Theorem 3.30]

We first illustrate a counterexample for [ 1, Theorem 3.26]. Consider the example [ 2, Example 2]. Let

where denotes the set of even natural numbers and denotes the set of odd natural numbers. Then and hence is semi-closed set in Let the complement of Then , the collection of all semi-open neighborhoods of in , but there does not exist such that because for any , contains an interval of the form , or for some .

Using the same example, we now refute [ 1, Theorem 3.27]. Let Then but there does not exist balanced such that . Hence, [ 1, Theorem 3.27] is not correct.

Finally, refuting [ 1, Theorem 3.30]. Consider [ 2, Example 2]. Let and , the set of natural numbers. Then and satisfy the hypothesis of [ 1, Theorem 3.30] but .

References

[1]  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.
In article      
 
[2]  M.D. Khan and M.A. Iqbal, On Irresolute Topological Vector Spaces, Adv. Pure Math. 6(2016), 105-112.
In article      View Article
 
[3]  M. Ram and S. Sharma, Corrigendum to: On Irresolute Topological Vector Spaces, New Trends in Mathematical Sciences, 6(4) (2018), 40-44.
In article      View Article
 

Published with license by Science and Education Publishing, Copyright © 2018 Madhu Ram

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Cite this article:

Normal Style
Madhu Ram. Correction to the Paper “On Irresolute Topological Vector Spaces-II”. Turkish Journal of Analysis and Number Theory. Vol. 6, No. 4, 2018, pp 124-124. http://pubs.sciepub.com/tjant/6/4/4
MLA Style
Ram, Madhu. "Correction to the Paper “On Irresolute Topological Vector Spaces-II”." Turkish Journal of Analysis and Number Theory 6.4 (2018): 124-124.
APA Style
Ram, M. (2018). Correction to the Paper “On Irresolute Topological Vector Spaces-II”. Turkish Journal of Analysis and Number Theory, 6(4), 124-124.
Chicago Style
Ram, Madhu. "Correction to the Paper “On Irresolute Topological Vector Spaces-II”." Turkish Journal of Analysis and Number Theory 6, no. 4 (2018): 124-124.
Share
[1]  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.
In article      
 
[2]  M.D. Khan and M.A. Iqbal, On Irresolute Topological Vector Spaces, Adv. Pure Math. 6(2016), 105-112.
In article      View Article
 
[3]  M. Ram and S. Sharma, Corrigendum to: On Irresolute Topological Vector Spaces, New Trends in Mathematical Sciences, 6(4) (2018), 40-44.
In article      View Article