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

Turkish Journal of Analysis and Number Theory. 2018, 6(4), 124-124. DOI: 10.12691/tjant-6-4-4
Received May 05, 2018; Revised July 06, 2018; Accepted August 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