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A topological space is sometimes said to exhibit a property locally, if the property is exhibited "near" each point in one of the following ways: Each point has a neighborhood exhibiting the property; Each point has a neighborhood base of sets exhibiting the property.
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In mathematics, the idea of a free object is one of the basic concepts of abstract algebra.Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A: the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure.
Local connectedness is, by definition, a local property of topological spaces, i.e., a topological property P such that a space X possesses property P if and only if each point x in X admits a neighborhood base of sets that have property P. Accordingly, all the "metaproperties" held by a local property hold for local connectedness. In particular:
Any free module is projective. The converse is true in the following cases: if R is a field or skew field: any module is free in this case. if the ring R is a principal ideal domain. For example, this applies to R = Z (the integers), so an abelian group is projective if and only if it is a free abelian group.
Following the lead of G-CORE and Morpheus, GQL aims to project the sub-graphs defined by matching patterns (and graphs then computed over those sub-graphs) as new graphs to be returned by a query. Patterns of this kind have become pervasive in property graph query languages, and are the basis for the advanced pattern sub-language being defined ...
AMSTERDAM (Reuters) -The head of the chemical weapons watchdog said on Thursday he would ask Syria's new leaders to grant investigators access to the country to continue work identifying ...
If you'd instead put your $10,000 into an S&P 500 (SNPINDEX: ^GSPC) index fund, you would've had just $11,900 at the end of the year. An equal investment in an S&P 500 index fund would be worth ...