20.500.12556/DKUM-91938 An embedding of the Cantor fan into the Lelek fan Ulaganje Cantorove lepeze u Lelekovu lepezu The Lelek fan L is usually constructed as a subcontinuum of the Cantor fan in such a way that the set of the end-points of L is dense in L. It easily follows that the Lelek fan is embeddable into the Cantor fan. It is also a well-known fact that the Cantor fan is embeddable into the Lelek fan, but this is less obvious. When proving this, one usually uses the well-known result by Dijkstra and van Mill that the Cantor set is embeddable into the complete Erdős space, and the well-known fact by Kawamura, Oversteegen, and Tymchatyn that the set of end-points of the Lelek fan is homeomorphic to the complete Erdős space. Then, the subcontinuum of the Lelek fan that is induced by the embedded Cantor set into the set of end-points of the Lelek fan, is a Cantor fan. In our paper, we give an alternative straightforward embedding of a Cantor fan into the Lelek fan. We do not use the fact that the Cantor set is embeddable into the complete Erdős space and that it is homeomorphic to the set of end-points of the Lelek fan. Instead, we use our recent techniques of Mahavier products of closed relations to produce an embedding of the Cantor fan into the Lelek fan. Since the Cantor fan is universal for the family of all smooth fans, it follows that also the Lelek fan is universal for smooth fans. Lelekova lepeza L obično se konstruira kao potkontinuum Cantorove lepeze na način da je skup krajnjih točaka od Lgust u L. Lako slijedi da je Lelekova lepeza uloživa u Cantorovu lepezu. Takodjer je dobro poznata činjenica da se Cantorova lepeza može uložiti u Lelekovu lepezu, ali to je manje očito. U dokazu te tvrdnje, obično se koristi dobro poznati rezultat Dijkstre i van Milla da je Cantorov skup uloživ u potpuni Erdősev prostor, te dobro poznata činjenica Kawamure, Oversteegena i Tymchatyna da je skup krajnjih točaka Lelekove lepeze homeomorfan potpunom Erdősevom prostoru. Zatim, potkontinuum Lelekove lepeze koji je induciran uloženim Cantorovim skupom u skup krajnjih točaka Lelekove lepeze je Cantorova lepeza. U našem radu dajemo alternativnu konstrukciju ulaganja Cantorove lepeze u Lelekovu lepezu. Ne koristimo se činjenicom da je Cantorov skup moguće uložiti u potpun Erdősev prostor i da je homeomorfan skupu krajnjih točaka Lelekove lepeze. Umjesto toga, koristimo naše nedavne tehnike Mahavierovih produkta zatvorenih relacija za ulaganje Cantorove lepeze u Lelekovu lepezu. Budući da je Cantorova lepeza univerzalna za klasu svih glatkih lepeza, slijedi da je i Lelekova lepeza univerzalna za glatke lepeze. closed relations Mahavier products fans Cantor fans Lelek fans zatvorene relacije Mahavierov produkt lepeza Cantorova lepeza Lelekova lepeza true false true Angleški jezik Hrvaški jezik Znanstveno delo 2025-03-04 09:59:14 2025-03-04 10:10:09 2025-03-05 03:09:18 0000-00-00 00:00:00 2025 0 0 Ključne besede v slovenščini: zaprta relacija, Mahavierjev produkt, pahljača, Cantorjeva pahljača, Lelekova pahljača str. 221-229 Letn. 29 = 564 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2023-05-12 2023-09-19 2025-01-01 519.17 227891971 10.21857/m8vqrt3lk9 1845-4100 RAZ_Banic_Iztok_2025.pdf RAZ_Banic_Iztok_2025.pdf 1 21F39F774A7F79563C4D06994B2F1953 7f02aef7a90ffed8134a42c7ff0208d47ef368d681314ef11ffa46d1f3840266 594c0a78-f8d8-11ef-bc66-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=188964 https://doi.org/10.21857/m8vqrt3lk9 1 f3f1f69b-f8d6-11ef-bc66-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=188963 Fakulteta za naravoslovje in matematiko 0 0 0