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Title: | How Many Closed Structures does the Construct PRAP Admit? | Authors: | Sioen, Mark | Keywords: | Pre-approach space (semi)-metric space; (symmetric) monoidal closed structure; measurable cardinal; strongly rigid class | Issue Date: | 2001 | Publisher: | Università degli Studi di Trieste. Dipartimento di Scienze Matematiche | Source: | Mark Sioen, "How Many Closed Structures does the Construct PRAP Admit?", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 32 (2001) suppl.2, pp. 135–147. | Series/Report no.: | Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics 32 (2001) suppl.2 |
Abstract: | We will prove that the topological construct PRAP, introduced by E. and R. Lowen in [9] as a numerification supercategory of the construct PRTOP of convergence spaces and continuous maps, admits a proper class of monoidal closed structures. We will even show that under the assumption that there does not exist a proper class of measurable cardinals, it admits a proper conglomerate (i.e. one which is not codable by a class) of mutually non-isomorphic monoidal closed structures. This severely contrasts with the situation concerning symmetric monoidal closed structures, because it is shown in [13] that PRAP only admits one symmetric tensorproduct, up to natural isomorphism. |
Type: | Article | URI: | http://hdl.handle.net/10077/4293 | ISSN: | 0049-4704 |
Appears in Collections: | Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.32 (2001) s2 |
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