{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T00:11:44Z","timestamp":1783901504527,"version":"3.55.0"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2014,3,30]],"date-time":"2014-03-30T00:00:00Z","timestamp":1396137600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-sa\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>\n                    In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of \u03b5\n                    <jats:sup>n<\/jats:sup>\n                    with a non-empty interior. This theorem states that, if T is a normal topological space, X is a closed subset of T, and A is a convex compact subset of \u03b5\n                    <jats:sup>n<\/jats:sup>\n                    with a non-empty interior, then a continuous function f : X \u2192 A can be extended to a continuous function g : T \u2192 \u03b5\n                    <jats:sup>n<\/jats:sup>\n                    . Additionally we show that a subset A is replaceable by an arbitrary subset of a topological space that is homeomorphic with a convex compact subset of En with a non-empty interior. This article is based on [20]; [23] and [22] can also serve as reference books.\n                  <\/jats:p>","DOI":"10.2478\/forma-2014-0002","type":"journal-article","created":{"date-parts":[[2015,5,28]],"date-time":"2015-05-28T16:26:02Z","timestamp":1432830362000},"page":"11-19","source":"Crossref","is-referenced-by-count":2,"title":["Tietze Extension Theorem for n-dimensional Spaces"],"prefix":"10.2478","volume":"22","author":[{"given":"Karol","family":"P\u0105k","sequence":"first","affiliation":[{"name":"Institute of Informatics University of Bia\u0142ystok Sosnowa 64, 15-887 Bia\u0142ystok Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2014,3,30]]},"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/22\/1\/article-p11.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/reference-global.com\/pdf\/10.2478\/forma-2014-0002","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T00:00:15Z","timestamp":1783900815000},"score":1,"resource":{"primary":{"URL":"https:\/\/reference-global.com\/article\/10.2478\/forma-2014-0002"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2014,3,30]]}},"alternative-id":["10.2478\/forma-2014-0002"],"URL":"https:\/\/doi.org\/10.2478\/forma-2014-0002","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,3,30]]}}}