Article: 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:

Question: What group operations must occur for group law and topology to integrate well?
Ans: continuous functions

Article: The end for the Laemmles came with a lavish version of Show Boat (1936), a remake of its earlier 1929 part-talkie production, and produced as a high-quality, big-budget film rather than as a B-picture. The new film featured several stars from the Broadway stage version, which began production in late 1935, and unlike the 1929 film was based on the Broadway musical rather than the novel. Carl, Jr.'s spending habits alarmed company stockholders. They would not allow production to start on Show Boat unless the Laemmles obtained a loan. Universal was forced to seek a $750,000 production loan from the Standard Capital Corporation, pledging the Laemmle family's controlling interest in Universal as collateral. It was the first time Universal had borrowed money for a production in its 26-year history. The production went $300,000 over budget; Standard called in the loan, cash-strapped Universal could not pay, Standard foreclosed and seized control of the studio on April 2, 1936.

Question: In what year had Universal previously made a version of Show Boat?
Ans: 1929

Article: Apple discontinued the use of PowerPC microprocessors in 2006. At WWDC 2005, Steve Jobs announced this transition, revealing that Mac OS X was always developed to run on both the Intel and PowerPC architectures. All new Macs now use x86 processors made by Intel, and some were renamed as a result. Intel-based Macs running OS X 10.6 and below (support has been discontinued since 10.7) can run pre-existing software developed for PowerPC using an emulator called Rosetta, although at noticeably slower speeds than native programs. However, the Classic environment is unavailable on the Intel architecture. Intel chips introduced the potential to run the Microsoft Windows operating system natively on Apple hardware, without emulation software such as Virtual PC. In March 2006, a group of hackers announced that they were able to run Windows XP on an Intel-based Mac. The group released their software as open source and has posted it for download on their website. On April 5, 2006, Apple announced the availability of the public beta of Boot Camp, software that allows owners of Intel-based Macs to install Windows XP on their machines; later versions added support for Windows Vista and Windows 7. Classic was discontinued in Mac OS X 10.5, and Boot Camp became a standard feature on Intel-based Macs.

Question: When did Apple discontinue the use of PowerPC microprocessors?
Ans: 2006

Article: Beta testing comes after alpha testing and can be considered a form of external user acceptance testing. Versions of the software, known as beta versions, are released to a limited audience outside of the programming team known as beta testers. The software is released to groups of people so that further testing can ensure the product has few faults or bugs. Beta versions can be made available to the open public to increase the feedback field to a maximal number of future users and to deliver value earlier, for an extended or even indefinite period of time (perpetual beta).[citation needed]

Question: What typically comes after the Alpha stage in the development and testing of software?
Ans:
Beta testing