162 research outputs found
Total Representations
Almost all representations considered in computable analysis are partial. We
provide arguments in favor of total representations (by elements of the Baire
space). Total representations make the well known analogy between numberings
and representations closer, unify some terminology, simplify some technical
details, suggest interesting open questions and new invariants of topological
spaces relevant to computable analysis.Comment: 30 page
Topological Complexity of omega-Powers : Extended Abstract
This is an extended abstract presenting new results on the topological
complexity of omega-powers (which are included in a paper "Classical and
effective descriptive complexities of omega-powers" available from
arXiv:0708.4176) and reflecting also some open questions which were discussed
during the Dagstuhl seminar on "Topological and Game-Theoretic Aspects of
Infinite Computations" 29.06.08 - 04.07.08
An Upper Bound on the Complexity of Recognizable Tree Languages
The third author noticed in his 1992 PhD Thesis [Sim92] that every regular
tree language of infinite trees is in a class
for some natural number , where is the game quantifier. We
first give a detailed exposition of this result. Next, using an embedding of
the Wadge hierarchy of non self-dual Borel subsets of the Cantor space
into the class , and the notions of Wadge degree
and Veblen function, we argue that this upper bound on the topological
complexity of regular tree languages is much better than the usual
Lipschitz and uniformly continuous reducibilities on ultrametric Polish spaces
We analyze the reducibilities induced by, respectively, uniformly continuous,
Lipschitz, and nonexpansive functions on arbitrary ultrametric Polish spaces,
and determine whether under suitable set-theoretical assumptions the induced
degree-structures are well-behaved.Comment: 37 pages, 2 figures, revised version, accepted for publication in the
Festschrift that will be published on the occasion of Victor Selivanov's 60th
birthday by Ontos-Verlag. A mistake has been corrected in Section
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