Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4293
Title: How Many Closed Structures does the Construct PRAP Admit?
Authors: Sioen, Mark
Keywords: Pre-approach space (semi)-metric space(symmetric) monoidal closed structuremeasurable cardinalstrongly 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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