Une méthode d'élimination des nombres transfinis des raisonnements mathématiques¶
Kuratowski, K. (1922). Une méthode d'élimination des nombres transfinis des raisonnements mathématiques. Fundamenta Mathematicae, 3(1), 76-108.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Idempotence
- … theory**, idempotent functions on a partially ordered set are called closure operators — `cl(cl(S)) = cl(S)` — and provide the foundation for topology (closure of a set), formal-language theory (Kleene closure), and Galois connections, with Tarski (1935) and Kuratowski (1922) supplying the canonical axiomatizations
This sourceKuratowski's lemma (every chain in a partially ordered set has an upper bound implies a maximal element exists); order-theoretic equivalent of the axiom of choice and Zorn's lemma.
- … theory**, idempotent functions on a partially ordered set are called closure operators — `cl(cl(S)) = cl(S)` — and provide the foundation for topology (closure of a set), formal-language theory (Kleene closure), and Galois connections, with Tarski (1935) and Kuratowski (1922) supplying the canonical axiomatizations
- Order
- In logic, proof theory, and foundations of mathematics, order underlies the well-ordering principle (equivalent to the axiom of choice; Kuratowski's (1922) lemma is a standard order-theoretic equivalent
This sourceKuratowski's lemma (every chain in a partially ordered set has an upper bound implies a maximal element exists); order-theoretic equivalent of the axiom of choice and Zorn's lemma.
- In logic, proof theory, and foundations of mathematics, order underlies the well-ordering principle (equivalent to the axiom of choice; Kuratowski's (1922) lemma is a standard order-theoretic equivalent
- Topology
- … every open set is a union of basis members; the open balls in a metric space form a basis for the metric topology), a subbasis (a collection whose finite intersections form a basis), a closure operator (a function $\overline{\cdot}: \mathcal{P}(X) \to \mathcal{P}(X)$ satisfying the four Kuratowski closure axioms
This sourceKuratowski's lemma (every chain in a partially ordered set has an upper bound implies a maximal element exists); order-theoretic equivalent of the axiom of choice and Zorn's lemma.
- … every open set is a union of basis members; the open balls in a metric space form a basis for the metric topology), a subbasis (a collection whose finite intersections form a basis), a closure operator (a function $\overline{\cdot}: \mathcal{P}(X) \to \mathcal{P}(X)$ satisfying the four Kuratowski closure axioms
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