...s the closure of an open set; in other words, it is the closure of its own interior $ \langle M\rangle $:
A set which is the interior of a closed set is called a canonical open set or $ \kappa o $-
2 KB (408 words) - 06:29, 30 May 2020
algebra (for example, the Borel $ \sigma $-
algebra) and containing exactly one representative from each orbit. However, if $
2 KB (240 words) - 19:40, 5 June 2020
...ological space $X$ with the Baire property is a [[Algebra of sets|$\sigma$-algebra]].
...first category (an open set is called ''regular'' if it coincides with the interior of its closure).
3 KB (414 words) - 13:42, 7 October 2012
The elements of the Lie algebra $ \mathfrak g $
is the operation of interior multiplication by $ X $
7 KB (1,006 words) - 08:24, 6 June 2020
...simple polygonal curve, so that non-adjacent sides have no common points (interior or end), then the polygon is called simple. If the boundary of a two-dimens
...he point is in the exterior domain, if it is odd, then the point is in the interior.
13 KB (2,146 words) - 22:23, 25 April 2012
...ion algebra $\mathcal{A} ( X )$ defined on $X$; cf. [[Algebra of functions|Algebra of functions]]) if each $f \in \mathcal{A} ( X )$ vanishing on $E$ can be a
Ditkin sets were first studied for the [[Fourier-algebra(2)|Fourier algebra]] $A ( \widehat { G } ) \cong L ^ { 1 } ( G )$, with the norm defined by $\
10 KB (1,614 words) - 16:56, 1 July 2020
...f functions|Algebra of functions]]). The algebra $A$ is called a Dirichlet algebra if $A + \overline{A}$ is uniformly dense in $C ( X )$. Dirichlet algebras w
...f D }$. The algebra $A ( \mathbf{D} )$ is a typical example of a Dirichlet algebra on the unit circle $\partial \mathbf{D}$. For $A ( \mathbf{D} )$, the measu
7 KB (1,114 words) - 19:36, 23 December 2023
[[Pseudo-Boolean algebra|Pseudo-Boolean algebra]]) or open sets in topological spaces (for intuitionistic logic), or elemen
where $\text{ Int }(X)$ denotes the interior of the set $X$.
3 KB (439 words) - 22:34, 16 June 2014
of maximal ideals of a [[Commutative Banach algebra|commutative Banach algebra]] $ A $
is a commutative Banach algebra containing $ A $
10 KB (1,551 words) - 08:37, 26 March 2023
$#C+1 = 179 : ~/encyclopedia/old_files/data/A011/A.0101370 Algebra of functions,
''function algebra''
11 KB (1,877 words) - 16:10, 1 April 2020
...t is called an ''[[ultrafilter]]'' (a maximal proper filter in any Boolean algebra is also called an ultrafilter).
...urhood]]s of any point $x \in E$ (the subsets of $E$ containing $x$ in the interior) form a filter.
3 KB (602 words) - 17:00, 25 September 2017
$#C+1 = 86 : ~/encyclopedia/old_files/data/P075/P.0705610 Pseudo\AAhBoolean algebra
Every pseudo-Boolean algebra is a [[Distributive lattice|distributive lattice]] with largest element 1 (
10 KB (1,402 words) - 08:08, 6 June 2020
form on the Lie algebra $ T _ {e} G $
of interior multiplication by $ \Omega $;
8 KB (1,110 words) - 16:10, 1 April 2020
...been successfully used in recent proofs of "deep" results in topological algebra (cf. also [[Separate and joint continuity|Separate and joint continuity]]),
3 KB (444 words) - 14:56, 1 May 2014
[[Banach algebra|Banach algebra]] $A$ over the field of complex numbers, with an involution $x \rightarrow
1) The algebra $C_0(X)$ of continuous complex-valued functions on a locally compact Hausd
15 KB (2,316 words) - 21:05, 20 April 2012
of parallel fields forms a subalgebra of the algebra of all tensor fields on $ M $
...t under contraction of tensor fields and permutation of their indices. The algebra $ \Pi ( M, \nabla ) $
8 KB (1,160 words) - 08:05, 6 June 2020
and analytic at interior points of $ E $).
is analytic at interior points of $ E $
18 KB (2,637 words) - 07:20, 26 March 2023
...an operator usually takes values in an algebra (in particular, an operator algebra) that is simpler than the original one.
has symbols of two types: interior and boundary. The interior symbol $ \sigma ^ {0} ( \mathfrak A ) $
13 KB (1,836 words) - 14:55, 7 June 2020
is decaying fast enough at infinity. ii) The interior problem, i.e. determining $ f $
in the interior of $ K $,
16 KB (2,342 words) - 17:25, 13 June 2020
multiplication) as well as interior (cup-multiplication). This is equivalent to the statement that the mapping
..., "A general algebraic approach to Steenrod operations" , ''The Steenrod Algebra and Its Applications'' , ''Lect. notes in math.'' , '''168''' , Springer (
8 KB (1,093 words) - 08:21, 13 January 2024