\u2208 ist eine Abk\u00fcrzung f\u00fcr Elementschaft (f\u00fcr Mengen)<\/p>\n\n\n\n
X<\/em> sei eine Menge. Definition von Uniformit\u00e4ten 1. X<\/em> ist eine Menge \u2227 ist eine Abk\u00fcrzung f\u00fcr \u00abund\u00bb \u2228 ist eine Abk\u00fcrzung f\u00fcr \u00aboder\u00bb \u00ac ist eine Abk\u00fcrzung f\u00fcr \u00abnicht\u00bb \u2192 ist eine Abk\u00fcrzung f\u00fcr \u00abwenn, dann\u00bb x, y, z, x1,x2, …, y1,y2,…,a, b, c, e und X, Y sind Variable f\u00fcr Mengen \u2208 ist eine Abk\u00fcrzung f\u00fcr Elementschaft (f\u00fcr Mengen) X sei eine Menge.a. \u0394 ( […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":14,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-fullwidth.php","meta":{"footnotes":""},"class_list":["post-3022","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages\/3022","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/comments?post=3022"}],"version-history":[{"count":15,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages\/3022\/revisions"}],"predecessor-version":[{"id":4909,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages\/3022\/revisions\/4909"}],"up":[{"embeddable":true,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages\/14"}],"wp:attachment":[{"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/media?parent=3022"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
a. \u0394 ( X<\/em> ) = {\u00a0\u2329 x<\/em>, x<\/em>\u00a0\u232a \/ x<\/em>\u00a0\u2208 X<\/em> }. \u0394 ( X<\/em> ) wird als die Diagonale \u00fcber<\/em> X<\/em> bezeichnet.
b. Sei u<\/em>\u00a0\u2286 X<\/em>\u00a0\u00d7 X<\/em> gegeben. u <\/em>-1<\/sup> = {\u00a0\u2329 y<\/em>, x<\/em>\u00a0\u232a \/ x<\/em>\u00a0\u2208 X<\/em>\u00a0\u2227 y<\/em>\u00a0\u2208 X<\/em>\u00a0\u2227\u00a0\u2329 x<\/em>, y<\/em>\u00a0\u232a\u00a0\u2208 u<\/em> }.
c. Seien u<\/em>1<\/sub>\u00a0\u2282\u00a0X<\/em>\u00a0\u00d7 X<\/em> und u<\/em>2<\/sub>\u00a0\u2282\u00a0X<\/em>\u00a0\u00d7 Y<\/em> gegeben.\u00a0u1<\/sub> <\/em>![\"\circ\"](\"https:\/\/theory-of-science.com\/de\/wp-content\/ql-cache\/quicklatex.com-480c54a62a2bca4764ae432eeefd784a_l3.png\" "\\"Rendered")
\u00a0u<\/em>2<\/sub> = {\u00a0\u2329 x<\/em>, z<\/em>\u00a0\u232a \/\u00a0\u2203 y<\/em> (\u00a0\u2329 x<\/em>, y<\/em>\u00a0\u232a\u00a0\u2208\u00a0u<\/em>1<\/sub>\u00a0\u2227\u00a0\u2329 y<\/em>, z<\/em>\u00a0\u232a\u00a0\u2208\u00a0u<\/em>2<\/sub> ) }.<\/p>\n\n\n\n
<\/strong>\u2329 X<\/em> , U<\/strong><\/em> \u232a ist eine Uniformit\u00e4t \u00fcber X<\/em> gdw<\/p>\n\n\n\n
2. U<\/strong> \u2282 X<\/em> \u00d7 X<\/em>
3. U<\/strong> \u2260 ![\"\emptyset\"](\"https:\/\/theory-of-science.com\/de\/wp-content\/ql-cache\/quicklatex.com-54833ab836cd28d9f1e2a624abe97b08_l3.png\" "\\"Rendered")
4. \u2200 u<\/em>1<\/sub>, u<\/em>2<\/sub> ( u<\/em>1<\/sub> \u2208 U<\/strong> \u2227 u<\/em>1<\/sub> \u2282 u<\/em>2<\/sub> \u2192 u<\/em>2<\/sub> \u2208 U<\/strong> )
5. \u2200 u<\/em>1<\/sub>, u<\/em>2<\/sub> ( u<\/em>1<\/sub> \u2208 U<\/strong> \u2227 u<\/em>2<\/sub> \u2208 U<\/strong> \u2192 u<\/em>1<\/sub> \u2229 u<\/em>2<\/sub> \u2208 U<\/strong> )
6. \u2200 u ( u \u2208 U<\/strong> \u2192 \u0394 ( Mp<\/sub><\/em> ) \u2282 u )
7. \u2200 u ( u \u2208 U<\/strong> \u2192 u <\/em>-1<\/sup> \u2208 U<\/strong> )
8. \u2200 u<\/em>1<\/sub> \u2208 U<\/strong> \u2203 u<\/em>2<\/sub> \u2208 U<\/strong> ( u<\/em>2<\/sub> u<\/em>2<\/sub> \u2286 u<\/em>1<\/sub> )<\/p>\n","protected":false},"excerpt":{"rendered":"