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COMPUTABILITY OF POLISH SPACES UP TO HOMEOMORPHISM
The Journal of Symbolic Logic, 2020AbstractWe study computable Polish spaces and Polish groups up to homeomorphism. We prove a natural effective analogy of Stone duality, and we also develop an effective definability technique which works up to homeomorphism. As an application, we show that there is a $\Delta ^0_2$ Polish space not homeomorphic to a computable one.
Matthew Harrison-Trainor +2 more
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The Space of Simple Configurations is Polish
Mathematical Notes, 2002For a noncompact, locally compact, connected, complete metric space \(M\), let \(\widehat\Gamma\) denote the configuration space with multiple points on \(M\) and let \(\Gamma\) denote the subset of simple configurations. Then the weak topology on \(\widehat\Gamma\) and the subspace topology on \(\Gamma\) are both separable and are both generated by ...
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Computability Theory on Polish Metric Spaces
The Bulletin of Symbolic Logic, 2023AbstractComputability theoretic aspects of Polish metric spaces are studied by adapting notions and methods of computable structure theory. In this dissertation, we mainly investigate index sets and classification problems for computably presentable Polish metric spaces.
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1995
A limit point of a topological space is a point that is not isolated, i.e., for every open nbhd U of x there is a point y ∈ U, y≠ x. A space is perfect if all its points are limit points. If P is a subset of a topological space X, we call P perfect in X if P is closed and perfect in its relative topology.
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A limit point of a topological space is a point that is not isolated, i.e., for every open nbhd U of x there is a point y ∈ U, y≠ x. A space is perfect if all its points are limit points. If P is a subset of a topological space X, we call P perfect in X if P is closed and perfect in its relative topology.
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Stopping problems on Polish spaces
1997The general theory of optimal stopping for a continuous-time Markov process is treated when the Markov process takes values in a Polish space. This extends results which are known for a locally compact state space. An application to a problem of mathematical finance is given.
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The space $$C_p(X)$$ is cofinally Polish if and only if it is pseudocomplete
Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2021V V Tkachuk, Tkachuk V V
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There are $$2^{\mathfrak {c}}$$ Quasicontinuous Non Borel Functions on Uncountable Polish Space
Results in Mathematics, 2021Ľubica Holá, Holá Ľubica
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