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In mathematics, upper hemicontinuity and lower hemicontinuity are extensions of the notions of upper and lower semicontinuity of single-valued functions to set-valued functions. A set-valued function that is both upper and lower hemicontinuous is said to be continuous in an analogy to the property of the same name for single-valued functions.
If M is a module over a ring R, then the support of M as a module coincides with the support of the associated quasicoherent sheaf ~ on the affine scheme Spec R. Moreover, if { U α = Spec ( R α ) } {\displaystyle \{U_{\alpha }=\operatorname {Spec} (R_{\alpha })\}} is an affine cover of a scheme X , then the support of a quasicoherent ...
If is a hemicompact space, then the space (,) of all continuous functions: to a metric space (,) with the compact-open topology is metrizable. [3] To see this, take a sequence ,, … of compact subsets of such that every compact subset of lies inside some compact set in this sequence (the existence of such a sequence follows from the hemicompactness of ).
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
In mathematics, a sheaf of O-modules or simply an O-module over a ringed space (X, O) is a sheaf F such that, for any open subset U of X, F(U) is an O(U)-module and the restriction maps F(U) → F(V) are compatible with the restriction maps O(U) → O(V): the restriction of fs is the restriction of f times the restriction of s for any f in O(U) and s in F(U).
The IUPAC numerical multiplier is a system of prefixes used in chemistry to indicate the number of atoms or groups in a molecule.
[6] [7] (review article) The Pauson–Khand reaction, which is conceptually similar, has also been shown to give improved results when hemilabile P,S type hybrid ligands were used. [ 8 ] Iridium(I) complexes incorporating hemilabile ligands which contain methoxy , dimethylamino , and pyridine as donor functions have been shown to be effective ...
Tetramethyl orthosilicate (TMOS) is the chemical compound with the formula Si(OCH 3) 4.This molecule consists of four methoxy groups bonded to a silicon atom. The basic properties are similar to the more popular tetraethyl orthosilicate, which is usually preferred because the product of hydrolysis, ethanol, is less toxic than methanol.