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Page "Probability space" ¶ 22
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** and is
** Eunectes murinus, the green anaconda, the largest species, is found east of the Andes in Colombia, Venezuela, the Guianas, Ecuador, Peru, Bolivia, Brazil and on the island of Trinidad.
** Eunectes notaeus, the yellow anaconda, a smaller species, is found in eastern Bolivia, southern Brazil, Paraguay and northeastern Argentina.
** Eunectes deschauenseei, the dark-spotted anaconda, is a rare species found in northeastern Brazil and coastal French Guiana.
** Eunectes beniensis, the Bolivian anaconda, the most recently defined species, is found in the Departments of Beni and Pando in Bolivia.
** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.
** The Cartesian product of any family of nonempty sets is nonempty.
** König's theorem: Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals.
** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.
** For every non-empty set S there is a binary operation defined on S that makes it a group.
** Tychonoff's theorem stating that every product of compact topological spaces is compact.
** In the product topology, the closure of a product of subsets is equal to the product of the closures.
** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.
** Any union of countably many countable sets is itself countable.
** If the set A is infinite, then there exists an injection from the natural numbers N to A ( see Dedekind infinite ).
** Every infinite game in which is a Borel subset of Baire space is determined.
** The Vitali theorem on the existence of non-measurable sets which states that there is a subset of the real numbers that is not Lebesgue measurable.
** The Lebesgue measure of a countable disjoint union of measurable sets is equal to the sum of the measures of the individual sets.
** The Nielsen – Schreier theorem, that every subgroup of a free group is free.

** and closed
** The closed unit ball of the dual of a normed vector space over the reals has an extreme point.
** The Baire category theorem about complete metric spaces, and its consequences, such as the open mapping theorem and the closed graph theorem.
** in a closed consensus process: Restricted membership and often having formal procedures for due-process among voting members
** Fundamental groups of closed orientable two-dimensional manifolds.
** The closed flute family, in which the musical instrument has a channel to form and direct the air stream over an edge.
** The U. S. Senate Committee on Armed Services and U. S. Senate Committee on Foreign Relations begins its closed door hearings into the dismissal of General Douglas MacArthur by U. S. President Harry S Truman.
** The Panama Canal is closed for a couple of weeks due to damage caused by earthquakes.
** Martial law is declared in Madrid, the University is closed and over 300 students are arrested.
** Adolf Hitler marries his longtime mistress Eva Braun in a closed civil ceremony in the Berlin Führerbunker.
** French President Charles De Gaulle states that French troops will be taken out of NATO and that all French NATO bases and HQ's must be closed within a year.
** is closed under complements: if A ∈, then also ( Ω ∖ A )∈,
** Birmingham Airport, UK ( opened 1984, closed 1995 )
** M-Bahn in Berlin, Germany ( opened in 1989, closed in 1991 )
** I went to the basketball court ; I was told it was closed for cleaning.
** Self-interested closed cliques and " old boy networks ".
** A snatch-block can be closed around a line, to grab the line, rather than threading the end of the line through the block.
** Old University of Louvain, a university founded in Leuven, Brabant, in 1425 and closed in 1797
** Orlando Air Force Base, now closed
** Hillsdale Elementary ( grades K-5 ) ( closed )
** Northwestern College, closed 1932
** Park Region Luther College, closed 1932
** Hudgens, open until recently, has been condemned for destruction and closed
** The Round, Newcastle upon Tyne ( closed 2008 )
** 08: 48: 40 UTC: Hatch on the airlock is closed and secured by Leonov.

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