https://topospaces.subwiki.org/w/index.php?action=history&feed=atom&title=Fuzzy_topological_spaceFuzzy topological space - Revision history2026-08-05T12:49:30ZRevision history for this page on the wikiMediaWiki 1.41.2https://topospaces.subwiki.org/w/index.php?title=Fuzzy_topological_space&diff=2770&oldid=prevVipul: New page: {{variation of|topological space}} ==Definition== A '''fuzzy topological space''' is a set <math>X</math> along with a collection <math>\delta</math> of subsets of <math>[0,1]^X</math> s...2008-12-09T03:18:48Z<p>New page: {{variation of|topological space}} ==Definition== A '''fuzzy topological space''' is a set <math>X</math> along with a collection <math>\delta</math> of subsets of <math>[0,1]^X</math> s...</p>
<p><b>New page</b></p><div>{{variation of|topological space}}<br />
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==Definition==<br />
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A '''fuzzy topological space''' is a set <math>X</math> along with a collection <math>\delta</math> of subsets of <math>[0,1]^X</math> satisfying:<br />
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* The constant functions <math>0</math> and <math>1</math> are in <math>\delta</math>.<br />
* For any two functions <math>A,B \in \delta</math>, the function <math>A \wedge B</math>, which sends each <math>x \in X</math> to <math>\min \{A(x), B(x)\}</math>, is also in <math>\delta</math>.<br />
* For any collection <math>A_i, i \in I</math>, of members of <math>\delta</math>, the function <math>\vee_i A_i</math>, which sends <math>x \in X</math> to <math>\max A_i(x)</math>, is also in <math>\delta</math>.<br />
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Such a collection of subsets is termed a '''fuzzy topology'''. The members of <math>\delta</math> are '''fuzzy open sets'''.</div>Vipul