Αναγραμματισμοί & Πληροφορίες σχετικά με | Αγγλικά λέξη BAIRE

Παραδείγματα χρήσης BAIRE σε μια πρόταση

• A space is a Baire space if the intersection of any countable collection of dense open sets is dense; see Baire space.
• A restricted form of the Baire category theorem, in which the complete metric space is also assumed to be separable, is provable in ZF with no additional choice principles.
• The notion of upper and lower semicontinuous function was first introduced and studied by René Baire in his thesis in 1899.
• This fact is important for the definition and use of nowhere dense subsets, meager subsets, and Baire spaces.
• One should note however that there are plenty of spaces that are Baire spaces without satisfying the conditions of the Baire category theorem, as shown in the Examples section below.
• By a result of Martin and Steel, existence of infinitely many Woodin cardinals implies projective determinacy, which in turn implies that every projective set is Lebesgue measurable, has the Baire property (differs from an open set by a meager set, that is, a set which is a countable union of nowhere dense sets), and the perfect set property (is either countable or contains a perfect subset).
• Common examples of Polish spaces are the real line, any separable Banach space, the Cantor space, and the Baire space.
• At the University he was mainly influenced by two professors, Gustave Dumas and Dmitry Mirimanoff, who guided him in studying the works of Émile Borel, René-Louis Baire, Henri Lebesgue, and Joseph Serret.
• The axiom of determinacy implies that for every subspace X of the real numbers, the Banach–Mazur game BM(X) is determined, and consequently, that every set of reals has the property of Baire.
• On October 25, 1868, during the Battle of Pino de Baire, Gómez led a machete charge on foot, ambushing a Spanish column and obliterating it; the Spanish suffered 233 casualties.
• Starting with his debut film, Apur Sansar (The Family of Apu, 1959), the third part of The Apu Trilogy, as adult Apu, he went on to work in several films with Ray, including Abhijan (The Expedition, 1962), Charulata (1964), Kapurush (1965), Aranyer Din Ratri (Days and Nights in the Forest, 1969), Ashani Sanket (Distant Thunder, 1973), Sonar Kella (The Fortress of Gold, 1974) and Joi Baba Felunath (The Elephant God, 1978) as Feluda, Hirak Rajar Deshe (1980), Ghare Baire (The Home and The World, 1984), Shakha Proshakha (1990) and Ganashatru (Enemy of the People, 1989).
• A homeomorphism between Baire space and the irrationals can be constructed using continued fractions.
• Already weaker versions of choice are sufficient: the Boolean prime ideal theorem implies that there is a nonprincipal ultrafilter on the set of natural numbers; each such ultrafilter induces, via binary representations of reals, a set of reals without the Baire property.
• Among the group's present actresses and actors are Swatilekha Sengupta, who starred in Satyajit Ray's movie Ghare Baire (The Home and the World) (1984) and Roland Joffé's City of Joy (1992), Goutam Halder, (he has left the group and formed a new one, initially becoming its director), Debshankar Halder, Sohini Sengupta, who acted in Aparna Sen's movie Paromitar Ek Din (2000), and Rudraprasad Sengupta himself.
• The Spanish Crown did not keep its part of the treaty with Cuba, and on February 24, 1895, insurgents rose against the Spaniards in the provinces of Oriente, Santa Clara and Matanzas in what became known as "El Grito de Baire".
• Satyajit Ray wrote a script for Ghare Baire in the 1940s, but the film, which was to have been directed by Harisadhan Dasgupta, was never made.
• In mathematics, Baire functions are functions obtained from continuous functions by transfinite iteration of the operation of forming pointwise limits of sequences of functions.
• There are several inequivalent definitions of Baire sets, but in the most widely used, the Baire sets of a locally compact Hausdorff space form the smallest σ-algebra such that all compactly supported continuous functions are measurable.
• Strong set-theoretic principles may be stated in terms of the determinacy of various pointclasses, which in turn implies that sets in those pointclasses (or sometimes larger ones) have regularity properties such as Lebesgue measurability (and indeed universal measurability), the property of Baire, and the perfect set property.
• Khandker was sued for accusing the Mujib Bahini of hooliganism and looting during the war in his book in his book 1971: Bhetore Baire.
• It includes the villages of Altos de Ventas, Anacahuita, America Libre, Baire, El Naranjo, Guaninao, La Maritonia, Laguna Blanca, Los Negros, Los Pasos, Maffo, Palo Seco, Pino de Baire, Pueblo Nuevo and Xavier.
• Baire function called also Baire measurable function: obtained from continuous functions by transfinite iteration of the operation of forming pointwise limits of sequences of functions.
• showed that if supercompact cardinals exist then every set of reals in L(R), the constructible sets generated by the reals, is Lebesgue measurable and has the Baire property; this includes every "reasonably definable" set of reals.
• El conflicto se inició el 24 de febrero de 1895 en un levantamiento simultáneo de treinta y cinco localidades cubanas, el llamado Grito de Baire, y finalizó en agosto de 1898, tras la entrada de Estados Unidos en el conflicto y la consiguiente derrota española.
• He contributed to the fields general topology, especially metrizable and Baire spaces, group theory of permutation groups and functional analysis, especially spectral theory, convexity in Hilbert spaces and normed rings.

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