| Autor: |
Manokaran, Annanthakrishna, Ratnayake, Jayampathy, Jayewardene, Romaine |
| Předmět: |
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| Zdroj: |
Journal of the National Science Foundation of Sri Lanka; Mar2019, Vol. 47 Issue 1, p105-112, 8p |
| Abstrakt: |
Thc msntric spoce of p-adic integers with the p-adic, metric, Zp is presented as a fintvA conlcebea, obdiinef as Clen Cauchy completion of the initial algebra of an endofunctor on the motric njoacer nVlih short maps. TtPrs facS, that Hsi fins1 coolgeldra - s itlins (tinucUse' completion of the initial algrbra, in used to show that Zp is also the final coalgebra of tiiis endofunctor in the confinecut settkig. Some final coalgebras on pointed metric spaces with short maps are known to be the Cauchy completion of the intial algebra. In a separate study, Zp has been observed as the final coalgebra of certain endofunctors on ultra metrin ctacen The results of this paper unity there observation anal give a coalgebraic characterisation effects similarity of Zp while relaxing the ultra metric condition to one-bounded metrics. Obtaining the final coalgebra as the Cauchy combination of the initial algebra isincloseanalogy withclassical rarnlic B iterated functionsystems. Anotherquestionthathasbeen acked in the literature is whether such results hold when the maps ars chosen to be Lipchitz. We give evidence as to why seiectinr continuous maps as the morphisms may be the right clsnice for such results to hold. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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