| Title: | The Lelek fan as the inverse limit of intervals with a single set-valued bonding function whose graph is an arc |
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| Authors: | ID Banič, Iztok (Author)
ID Erceg, Goran (Author)
ID Kennedy, Judy A. (Author) |
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| Files: |  Banic-2023-The_Lelek_Fan_as_the_Inverse_Limit.pdf (504,26 KB)
MD5: B56E9D5E4A927E97B9917391F60B054F
 https://doi.org/10.1007/s00009-023-02323-3
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | We consider a family of inverse limits of inverse sequences of closed unit intervals with a single upper semi-continuous set-valued bonding function whose graph is an arc; the graph is the union of two line segments in [0,1]2, both of which contain the origin (0, 0) and have positive slope. One of the segments extends to the top-boundary and the other to the right side boundary of [0,1] x [0,1]. We show that there is a large subfamily F of these bonding functions such that for each fEF, the inverse limit of the inverse sequence of closed unit intervals using f as a single bonding function is homeomorphic to the Lelek fan. |
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| Keywords: | fan, cantor fan, Lelek fan, closed relation, Mahavier product, inverse limit, set-valued function |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 07.06.2022 |
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| Article acceptance date: | 12.01.2023 |
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| Publication date: | 16.03.2023 |
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| Publisher: | Birkhäuser |
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| Year of publishing: | 2023 |
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| Number of pages: | Str. 1-24 |
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| Numbering: | Letn. 20, Št. 3, št. članka 159 |
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| PID: | 20.500.12556/DKUM-87388  |
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| UDC: | 519.17 |
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| ISSN on article: | 1660-5446 |
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| COBISS.SI-ID: | 148424195 |
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| DOI: | 10.1007/s00009-023-02323-3 |
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| Publication date in DKUM: | 14.03.2024 |
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| Views: | 737 |
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| Downloads: | 542 |
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| Metadata: |    |
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| Categories: | Misc.
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