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Keywords:
Chigogidze extension of functors; 1-preimage preserving property
Chigogidze extension of functors; 1-preimage preserving property
Summary:
A. Chigogidze defined for each normal functor on the category Comp an extension which is a normal functor on the category Tych. We consider this extension for any functor on the category Comp and investigate which properties it preserves from the definition of normal functor. We investigate as well some topological properties of such extension.
References:
[1] Banakh T.: Descriptive classes of sets and topological functors. Ukrain. Mat. Zh. 47 (1995), 408–410. DOI 10.1007/BF01056310 | MR 1353221 | Zbl 0887.46041
[2] Banakh T., Cauty R.: Topological classification of spaces of probability measures over coanalytic sets. Mat. Zametki 55 (1994), 10–19 (Russian). MR 1275298
[3] Banakh T., Klymenko M., Kucharski A.: On functors preserving skeletal maps and skeletally generated compacta. in preparation.
[4] Banakh T., Radul T., Zarichnyi M.: Absorbing Sets in Infinite-dimensional Manifolds. VNTL Publishers, Lviv, 1996. MR 1719109 | Zbl 1147.54322
[5] Camargo J.: The functor of nonexpanding functionals. Rev. Integr. Temas Mat. 20 (2002), 1–12 (Spanish). MR 2253170
[6] Chigogidze A.: On extension of normal functors. Vestnik Moskov. Univ. Mat. Mekh. 6, (1984), 23–26 (Russian). MR 0775298
[7] Curtis D.W., Dobrowolski T., Mogilski J.: Some applications of the topological characterizations of the sigma-compact spaces $l_2^f$ and $\Sigma $. Trans. Amer. Math. Soc. 284 (1984), 837–846. MR 0743748
[8] Dobrowolski T.: The compact Z-property in convex sets. Topology Appl. 23 (1986), 163–172. DOI 10.1016/0166-8641(86)90038-6 | MR 0855456
[9] Fedorchuk V., Zarichnyi M.: Covariant functors in categories of topological spaces. Results of Science and Technics, Algebra. Topology. Geometry, vol. 28, 47–95 (Russian), Moscow, 1990. MR 1059477
[10] Radul T.: On the functor of order-preserving functionals. Comment. Math. Univ. Carolin. 39 (1998), 609–615. MR 1666806 | Zbl 0962.54009
[11] Radul T.: On strongly Lawson and I-Lawson monads. Bol. Mat. (N.S.) 6 (1999), 69–75. MR 1859108 | Zbl 1203.18008
[12] Radul T.: On functional representations of Lawson monads. Appl. Categ. Structures 9 (2001), 457–463. DOI 10.1023/A:1012052928198 | MR 1865611
[13] Teleiko A., Zarichnyi M.: Categorical Topology of Compact Hausdorff Spaces. VNTL Publishers, Lviv, 1999. MR 1783651 | Zbl 1032.54004
[14] Shapiro L.: On operators of extension of functions and normal functors. Vestnik Moskov. Univ. 1 (1992), 35–42 (Russian). MR 1214589
[15] Schepin E.: Functors and uncountable powers of compacta. Uspekhi Mat. Nauk 36 (1981), 3–62 (Russian). MR 0622720
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