{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T11:33:55Z","timestamp":1771673635733,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,6,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n\t\t\t\t<jats:p>We first provide a modified version of the proof in [3] that\nthe Sorgenfrey line is <jats:italic>T<\/jats:italic><jats:sub>1<\/jats:sub>. Here, we prove that it is in fact T2, a stronger result.\nNext, we prove that all subspaces of \u211d<jats:sup>1<\/jats:sup> (that is the real line with the usual\ntopology) are Lindel\u00a8of. We utilize this result in the proof that the Sorgenfrey\nline is Lindel\u00a8of, which is based on the proof found in [8]. Next, we construct the\nSorgenfrey plane, as the product topology of the Sorgenfrey line and itself. We\nprove that the Sorgenfrey plane is not Lindel\u00a8of, and therefore the product space\nof two Lindel\u00a8of spaces need not be Lindel\u00a8of. Further, we note that the Sorgenfrey\nline is regular, following from [3]:59. Next, we observe that the Sorgenfrey line is\nnormal since it is both regular and Lindel\u00a8of. Finally, we prove that the Sorgenfrey\nplane is not normal, and hence the product of two normal spaces need not be\nnormal. The proof that the Sorgenfrey plane is not normal and many of the\nlemmas leading up to this result are modelled after the proof in [3], that the\nNiemytzki plane is not normal. Information was also gathered from [15].<\/jats:p>","DOI":"10.2478\/forma-2013-0009","type":"journal-article","created":{"date-parts":[[2014,1,9]],"date-time":"2014-01-09T20:14:15Z","timestamp":1389298455000},"page":"83-85","source":"Crossref","is-referenced-by-count":1,"title":["Some Properties of the Sorgenfrey Line and the Sorgenfrey Plane"],"prefix":"10.2478","volume":"21","author":[{"given":"Adam St.","family":"Arnaud","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Piotr","family":"Rudnicki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","container-title":["Formalized Mathematics"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/21\/2\/article-p83.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/forma.2013.21.issue-2\/forma-2013-0009\/forma-2013-0009.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T16:17:28Z","timestamp":1590769048000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/forma-2013-0009"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6,1]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.2478\/forma-2013-0009","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2013,6,1]]}}}