منابع مشابه
Playing 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 کاملFormally 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 کاملSolutions of initial and boundary value problems via F-contraction mappings in metric-like space
We present sufficient conditions for the existence of solutions of second-order two-point boundary value and fractional order functional differential equation problems in a space where self distance is not necessarily zero. For this, first we introduce a Ciric type generalized F-contraction and F- Suzuki contraction in a metric-like space and give relevance to fixed point results. To illustrate...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2000
ISSN: 0196-8858
DOI: 10.1006/aama.1999.0690