Problem: Some topological spaces may be endowed with a group law. In order for the group law and the topology to interweave well, the group operations must be continuous functions, that is, g h, and g1 must not vary wildly if g and h vary only little. Such groups are called topological groups, and they are the group objects in the category of topological spaces. The most basic examples are the reals R under addition, (R {0}, ), and similarly with any other topological field such as the complex numbers or p-adic numbers. All of these groups are locally compact, so they have Haar measures and can be studied via harmonic analysis. The former offer an abstract formalism of invariant integrals. Invariance means, in the case of real numbers for example:
What are topological spaces categorized by?
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Answer: unanswerable

Problem: Affirmative action in the United States tends to focus on issues such as education and employment, specifically granting special consideration to racial minorities, Native Americans, and women who have been historically excluded groups in America. Reports have shown that minorities and women have faced discrimination in schools and businesses for many years and this discrimination produced unfair advantages for whites and males in education and employment. The impetus toward affirmative action is redressing the disadvantages associated with past and present discrimination. Further impetus is a desire to ensure public institutions, such as universities, hospitals, and police forces, are more representative of the populations they serve.
Studies showed that discrimination in both business sectors and education resulted in disadvantages for what group of people?
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Answer: unanswerable

Problem: All of Chopin's compositions include the piano. Most are for solo piano, though he also wrote two piano concertos, a few chamber pieces, and some songs to Polish lyrics. His keyboard style is highly individual and often technically demanding; his own performances were noted for their nuance and sensitivity. Chopin invented the concept of instrumental ballade. His major piano works also include mazurkas, waltzes, nocturnes, polonaises, etudes, impromptus, scherzos, preludes and sonatas, some published only after his death. Influences on his compositional style include Polish folk music, the classical tradition of J. S. Bach, Mozart and Schubert, the music of all of whom he admired, as well as the Paris salons where he was a frequent guest. His innovations in style, musical form, and harmony, and his association of music with nationalism, were influential throughout and after the late Romantic period.
What instrument is involved in all of Chopin's work?
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Answer:
piano