of analytic spaces such that for certain analytic sets $ S \subset X $
f : X \setminus S \rightarrow Y \setminus T \ \
1 KB (175 words) - 08:01, 6 June 2020
...then, for every chart $(U, \phi)$ in the atlas defining $N$, $\phi (U\cap S)$ is a set of (Lebesgue) measure zero.
...ger set|meager set]]. The latter statement is also sometimes called ''Sard's theorem'': however it is not equivalent to the one above, since closed meag
1 KB (203 words) - 16:38, 17 November 2012
\frac{x - s }{2}
0 \leq x, s \leq 2 \pi .
902 bytes (131 words) - 20:27, 18 March 2024
\xi(s) = \frac12 s(s-1) \pi^{-s/2} \Gamma(s/2) \zeta(s)
with $\zeta(s)$ the Riemann zeta function. The Riemann hypothesis is equivalent to the a
2 KB (247 words) - 20:25, 20 November 2023
...ly transitively on the set of all chambers and is generated by the set $ S $
moreover, the pair $ ( W , S ) $
4 KB (631 words) - 16:43, 4 June 2020
...ose of $\pi$. Eilenberg–MacLane spaces were introduced by S. Eilenberg and S. MacLane .
.../TD></TR><TR><TD valign="top">[1b]</TD> <TD valign="top"> S. Eilenberg, S. MacLane, "Relations between homology and homotopy groups of spaces. II"
2 KB (272 words) - 13:05, 24 December 2020
...$E\subset \mathbb{R}$ is a non-empty bounded set, $E_a^b=\{s \in E: a \leq s \leq b \}$ for $a,b \in E$ ($a \leq b$), $X$ is a metric space with a metri
...rem.''' Let ${E_t}^-=\{s \in E: s \leq t\}$ and ${E_t}^+=\{s \in E: t \leq s\}$. The following conditions are equivalent:
2 KB (413 words) - 17:07, 21 April 2016
$$\def\s{\sigma}\a(cx)=c^\s\a(x)$$
...g of vector spaces over the field $\C$ relative to complex conjugation $c^\s = \bar c$ is also known as an anti-linear mapping. A semi-linear mapping of
2 KB (264 words) - 22:23, 2 November 2013
$#C+1 = 12 : ~/encyclopedia/old_files/data/S086/S.0806710 Spherical indicatrix
under a mapping from the points of the curve onto the unit sphere $ S ^ {2} $
2 KB (378 words) - 08:22, 6 June 2020
...ies $\sum_{n=0}^\infty a_n$ can be summed by Riemann's method to a number $S$ if
...o0}\left[a_0+\sum_{n=1}^\infty a_n\left(\frac{\sin nh}{nh}\right)^2\right]=S.$$
2 KB (300 words) - 16:17, 4 October 2014
...always a result of an earlier calculation once one inputs $ \pi _ {1} ( S ^ {1} ) $.
It has been used to calculate $ \pi _ {n + i } ( S ^ {n} ) $
6 KB (927 words) - 19:36, 5 June 2020
( a b ) ^ {n} = a ^ {n} b ^ {n} s _ {1} ^ {n} \dots s _ {t} ^ {n}
holds, where $ s _ {1} \dots s _ {t} $
2 KB (283 words) - 08:10, 6 June 2020
\frac{\partial f }{\partial s }
= - A _ {s} f
5 KB (778 words) - 22:14, 5 June 2020
is a submonoid $ S $
of $ R $ (i.e. $ 1 \in S $
4 KB (674 words) - 07:14, 12 July 2022
A semi-group $ S $
as an ideal). To each element $ s $
4 KB (623 words) - 19:38, 5 June 2020
...ur sides $a$, $b$, $c$, $d$ intersecting in the six points $P$, $Q$, $R$, $S$, $T$, $U$. Then the three circles that have the three diagonals $PS$, $QT$
...n="top">[a1]</TD> <TD valign="top"> R. Fritsch, "Remarks on Bodenmiller's theorem" ''J. of Geometry'' , '''47''' (1993) pp. 23–31</TD></TR><TR><
816 bytes (120 words) - 08:29, 26 March 2023
that occur. Set $ S _ {0} = S _ {0,n} = 1 $
S _ {j} = S _ { j,n} = \sum {\mathsf P} ( A _ {i _ 1 } \cap \dots \cap A _ { i _ j } )
4 KB (657 words) - 12:53, 6 May 2023
A function $ K( x, s) $,
$ a \leq x, s \leq b $,
1,003 bytes (146 words) - 08:04, 6 June 2020
...the alphabet. From an alphabet we may obtain '''strings''' (or '''[[word]]s''') which are finite [[Sequence|sequences]] of letters over $\Sigma$. The e
...''' of $\Sigma$ (or '''monoid closure''') after the American mathematician S. C. Kleene. The set $\Sigma^* \setminus \{ \lambda\}$ is denoted $\Sigma^+$
2 KB (266 words) - 07:58, 18 November 2023
In the above, an almost-periodic trajectory in a [[dynamical system]] $\{ S^t \}$ on a metric space $(X,\rho)$ is the trajectory of any point $x \in X$
\left\lbrace{ \tau \in \mathbb{R} : \rho(S^t(x), S^{t+\tau}(x)) < \epsilon \ \text{for}\ -\infty < t < +\infty }\right\rbrace
1,020 bytes (154 words) - 19:16, 25 October 2014