<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-interdisciplinary-mathematics</journal-id>
      <journal-title-group>
        <journal-title>Journal of Interdisciplinary Mathematics</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-012X</issn>
      <issn publication-format="print">0972-0502</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIM-1738</article-id>
      <title-group>
        <article-title>Regularity and normality of nano topological spaces modeled by pre-open sets structures</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Hussein</surname>
            <given-names>Ghufran Ali</given-names>
          </name>
          <aff>Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Babylon, Iraq</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Al-Nafie</surname>
            <given-names>Z. D.</given-names>
          </name>
          <aff>Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Babylon, Iraq</aff>
        </contrib>
      </contrib-group>
      <volume>27</volume>
      <issue>4</issue>
      <fpage>667</fpage>
      <lpage>673</lpage>
      <pub-date date-type="pub">
        <day>30</day>
        <month>06</month>
        <year>2024</year>
      </pub-date>
      <abstract>
        <p>A new class of Nano topological spaces, termed nano pre-open sets, are presented and explored in this article. Since the Nano topology contains at most five sets, we establish new structures of nano open sets and nano open covers and new requirement concepts are discussed like Nano pre-open covers, Nano pre- T_0, T_1, T_2. In this work, regularity and normality are defined as follows: Nano pre-regular and Nano pre-normal spaces. Many new theorems are stated and proved.</p>
      </abstract>
      <kwd-group>
        <kwd>Nano topology</kwd>
        <kwd>Regularity space</kwd>
        <kwd>Normality space</kwd>
        <kwd>Pre-open</kwd>
        <kwd>Separation axioms</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
