Hyperspace as intersection of inclusion hyperspaces and idempotent measures

T.M.Radul

We prove that the hyperspace $\exp X$ of a compact space $X$ can be obtained as the inter\-sec\-tion of the space $GX$ of inclusion hyperspaces over $X$ and the space $I X$ of idempotent measures on $X$.

1. S.~Eilenberg, J.~Moore, Adjoint functors and triples, Illinois J.Math. 9 (1965) 381--389.

2. A.~Teleiko, M.~Zarichnyi, Categorical Topology of Compact Hausdorff Spaces, VNTL Publishers. Lviv, 1999.

3. T.~Radul, M.M.~Zarichnyi, Monads in the category of compacta, Uspekhi Mat. Nauk. 50 (1995) №3, 83--108.

4. L.B.~Shapiro, On function extension operators and normal functors, Vestnik Moskov. Univ. Ser. I Mat. Mech. (1992) №1, 35--42 (in Russian).

5. T.~Radul, A functional representation of the hyperspace monad, Comment.~Math.~Univ.~Carolin. 38 (1997) 165--168.

6. T.~Radul, On functional representations of Lawson monads, Appl. Categ. Structures 9 (2001) 457--463.

7. M.~Zarichnyi, Idempotent probability measures, I, preprint (arXiv:math/0608754v1), 2007.

8. T.~Radul, On the functor of order-preserving functionals, Comment. Math. Univ. Carolin. 39 (1998) 609--615.

9. T.~Radul, Monad of hyperspaces of inclusion and its algebras, Ukrain. Mat. Zh. 42 (1990) 806--812.

	Hyperspace as intersection of inclusion hyperspaces and idempotent measures
Author	T.M.Radul tarasradul@yahoo.co.uk Department of Mechanics and Mathematics,Ivan Franko National University of Lviv
Abstract	We prove that the hyperspace $\exp X$ of a compact space $X$ can be obtained as the inter\-sec\-tion of the space $GX$ of inclusion hyperspaces over $X$ and the space $I X$ of idempotent measures on $X$.
Keywords	inclusion hyperspace, intersection, idempotent measure
DOI	doi:10.30970/ms.31.2.207-210
Reference	1. S.~Eilenberg, J.~Moore, Adjoint functors and triples, Illinois J.Math. 9 (1965) 381--389. 2. A.~Teleiko, M.~Zarichnyi, Categorical Topology of Compact Hausdorff Spaces, VNTL Publishers. Lviv, 1999. 3. T.~Radul, M.M.~Zarichnyi, Monads in the category of compacta, Uspekhi Mat. Nauk. 50 (1995) №3, 83--108. 4. L.B.~Shapiro, On function extension operators and normal functors, Vestnik Moskov. Univ. Ser. I Mat. Mech. (1992) №1, 35--42 (in Russian). 5. T.~Radul, A functional representation of the hyperspace monad, Comment.~Math.~Univ.~Carolin. 38 (1997) 165--168. 6. T.~Radul, On functional representations of Lawson monads, Appl. Categ. Structures 9 (2001) 457--463. 7. M.~Zarichnyi, Idempotent probability measures, I, preprint (arXiv:math/0608754v1), 2007. 8. T.~Radul, On the functor of order-preserving functionals, Comment. Math. Univ. Carolin. 39 (1998) 609--615. 9. T.~Radul, Monad of hyperspaces of inclusion and its algebras, Ukrain. Mat. Zh. 42 (1990) 806--812.
Pages	207-210
Volume	31
Issue	2
Year	2009
Journal	Matematychni Studii
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