منابع مشابه
Formally continuous functions on Baire space
A function from Baire space N to the natural numbers N is called formally continuous if it is induced by a morphism between the corresponding formal spaces. We compare formal continuity to two other notions of continuity on Baire space working in Bishop constructive mathematics: one is a function induced by a Brouwer-operation (i.e. inductively defined neighbourhood function); the other is a fu...
متن کاملPlaying Games in the Baire Space
We solve a generalized version of Church’s Synthesis Problem where a play is given by a sequence of natural numbers rather than a sequence of bits; so a play is an element of the Baire space rather than of the Cantor space. Two players Input and Output choose natural numbers in alternation to generate a play. We present a natural model of automata (“N-memory automata”) equipped with the parity ...
متن کاملCompact subsets of the Baire space
Let P be the natural forcing for producing a finite splitting tree using finite conditions. Namely, p ∈ P iff p ⊆ ω is a finite subtree and p ≤ q iff p ⊇ q is an end extension of q. End extension means if s ∈ p\q then s ⊇ t for some t ∈ q which is terminal in q, i.e., has no extensions in q. This order is countable and hence forcing equivalent to adding a single Cohen real. The union of P-gener...
متن کاملComputable Analysis Over the Generalized Baire Space
One of the main goals of computable analysis is that of formalizing the complexity of theorems from real analysis. In this setting Weihrauch reductions play the role that Turing reductions do in standard computability theory. Via coding, we can transfer computability and topological results from the Baire space ω to any space of cardinality 2א0 , so that e.g. functions over R can be coded as fu...
متن کاملA hierarchy of clopen graphs on the Baire space
We say that E ⊆ X × X is a clopen graph on X iff E is symmetric and irreflexive and clopen relative to X\∆ where ∆ = {(x, x) : x ∈ X} is the diagonal. Equivalently E ⊆ [X] and for all x 6= y ∈ X there are open neighborhoods x ∈ U and y ∈ V such that either U × V ⊆ E or U × V ⊆ X\E. For clopen graphs E1, E2 on spaces X1, X2, we say that E1 continuously reduces to E2 iff there is a continuous map...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1972
ISSN: 0002-9939
DOI: 10.2307/2038200