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Selection Principle
In mathematics, a selection principle is a rule asserting the possibility of obtaining mathematically significant objects by selecting elements from given sequences of sets. The theory of selection principles studies these principles and their relations to other mathematical properties. Selection principles mainly describe covering properties, measure- and category-theoretic properties, and local properties in topological spaces, especially function spaces. Often, the characterization of a mathematical property using a selection principle is a nontrivial task leading to new insights on the characterized property. The main selection principles In 1924, Karl Menger introduced the following basis property for metric spaces: Every basis of the topology contains a sequence of sets with vanishing diameters that covers the space. Soon thereafter, Witold Hurewicz observed that Menger's basis property is equivalent to the following selective property: for every sequence of op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anthropic Principle
The anthropic principle, also known as the "observation selection effect", is the hypothesis, first proposed in 1957 by Robert Dicke, that there is a restrictive lower bound on how statistically probable our observations of the universe are, because observations could only happen in a universe capable of developing intelligent life. Proponents of the anthropic principle argue that it explains why this universe has the age and the fundamental physical constants necessary to accommodate conscious life, since if either had been different, we would not have been around to make observations. Anthropic reasoning is often used to deal with the notion that the universe seems to be finely tuned for the existence of life. There are many different formulations of the anthropic principle. Philosopher Nick Bostrom counts them at thirty, but the underlying principles can be divided into "weak" and "strong" forms, depending on the types of cosmological claims they entail. The weak anthropic p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
