Geodesic
Variations on the~Wadge Reducibility
Matematičeskie trudy, Tome 8 (2005) no. 1, pp. 135-175

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The Wadge reducibility in the Baire and Cantor spaces is very important in descriptive set theory. We consider the Wadge reducibility in some other topological spaces, in particular, in the $\varphi$-spaces which are topological counterparts of the algebraic directed-complete partial orderings. It turns out that the Wadge reducibility behaves worse in most spaces than in the classical case but there exist interesting examples of spaces with a better behavior as well. 
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     author = {V. L. Selivanov},
     title = {Variations on {the~Wadge} {Reducibility}},
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V. L. Selivanov. Variations on the~Wadge Reducibility. Matematičeskie trudy, Tome 8 (2005) no. 1, pp. 135-175. http://geodesic.mathdoc.fr/item/MT_2005_8_1_a4/