|
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 Set (mathematics), sets. The theory of selection principles studies these principles and their relations to other mathematical properties. Selection principles mainly describe covering properties, measure theory, 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 Reprinted in ''Selecta Mathematica I'' (2002), , , pp. 155-178. introduced the following basis property for metric spaces: Every basis (topology), basis of the topology contains a sequence of sets with vanishing diameters that covers the space. Soon thereafter, Witold Hurewicz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anthropic Principle
In cosmology, the anthropic principle, also known as the observation selection effect, is the proposition that the range of possible observations that could be made about the universe is limited by the fact that observations are only possible in the type of universe that is capable of developing observers in the first place. Proponents of the anthropic principle argue that it explains why the universe has the age and the fundamental physical constants necessary to accommodate intelligent life. If either had been significantly different, no one would have been around to make observations. Anthropic reasoning has been used to address the question as to why certain measured physical constants take the values that they do, rather than some other arbitrary values, and to explain a perception that the universe appears to be finely tuned for the existence of life. There are many different formulations of the anthropic principle. Philosopher Nick Bostrom counts thirty, but the underlying ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
