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• Orientation of manifolds
  Patches are open so if they intersect, they have to overlap! Indeed, if $U \cap V \neq \emptyset$ then $U \cap V$ is open. Hence on $U \cap V$ there are two coordinate systems, from $U$ and from $V
  6 KB (983 words) - 16:30, 28 January 2013
• Vector and complex variables
  '''Example.''' There are even more outcomes that the theorem doesn't cover. Recall the characteristic polynomial of the matrix $A$ of the $90$ degree for all $z$ in an open disk $D$ around $a$ and such that the series $\sum_{n=0}^{\infty}M_n$ (of r
  113 KB (18,750 words) - 02:33, 10 December 2018
• Geometry in calculus
  ...o a}f(x)=L$ if for any open [[neighborhood]] $\epsilon$ of $L$ there is an open neighborhood $\delta$ of $a$ such that $x\in\delta$ implies $f(x)\in\epsilo <center>for any $\epsilon >0$ there is open [[cover]] $\delta$ of $[a,b]$ such that $|I-R(P)|<\epsilon$ whenever all elements o
  9 KB (1,604 words) - 18:08, 27 August 2015
• Differential calculus of parametric curves
  for all $t$ within some open interval from $t=s$; second: '''Definition.''' Suppose a parametric curve $X=F(t)$ is defined on an open interval $I$ that contains $t=s$. Then the ''derivative'' of $F$ at $t=s$ i
  130 KB (22,842 words) - 13:52, 24 November 2018
• Calculus as a part of topology
  ...o a}f(x)=L$ if for any open [[neighborhood]] $\epsilon$ of $L$ there is an open neighborhood $\delta$ of $a$ such that $x\in\delta$ implies $f(x)\in\epsilo *for any $\epsilon >0$ there is open cover $\delta$ of $[a,b]$ such that $|I-R(P)|<\epsilon$ whenever all elements of
  13 KB (2,233 words) - 14:41, 20 February 2015
• Social choice
  ...ical creeds).''' The six statements below are meant to represent an open ''cover'' of the political spectrum (in the US). In other words, we assume that eve We now build the nerve of this cover. The intersections become the vertices and the sets become the edges:
  47 KB (8,030 words) - 18:48, 30 November 2015
• Elections
  Therefore, the nerve of this cover will contain an edge between these two vertices. Then the space of choices The open cover $\alpha$ is still the collection of $U_{ij}$ but this time there are no emp
  33 KB (5,872 words) - 13:13, 17 August 2015
• The derivative
  ...ee the tangent line as an edge of a piece of paper; then this piece has to cover none of the (relevant) part of the graph: (B) If a function is constant on an open interval $I$, then its derivative is zero for all $x$ in $I$; i.e.,
  75 KB (13,000 words) - 15:12, 7 December 2018
• Test
  #[[Open and closed sets]] #Approximate topological spaces: [[Nerve of cover]]
  16 KB (2,139 words) - 23:01, 9 February 2015
• From continuity to point-set topology
  These sets are open intervals but can be also seen as "balls": *$\gamma _X$ is the set of all open balls in $X={\bf R}^n$, and
  7 KB (1,207 words) - 13:01, 12 August 2015
• Conferences and workshops
  ...s are perfect for enriching courses in these areas. Some of topics we will cover include the geometry and combinatorics of polytopes, triangulations, combin ...s a tremendous amount of work going on currently, and one can easily state open problems. It also has important applications to chemistry, biochemistry and
  8 KB (1,122 words) - 02:52, 24 October 2011
• Applied Topology and Geometry
  #[[Open and closed sets]] #Approximate topological spaces: [[Nerve of cover]]
  16 KB (2,088 words) - 16:37, 29 November 2014
• Axioms of chain complexes
  ...e the chain complex. That is, if $(X,A)$ is a pair and $\gamma$ is an open cover of $X$, then the chain map generated by the [[inclusion]] of the sum of sub
  4 KB (592 words) - 14:13, 4 August 2013
• Singular chain complexes
  '''Theorem (Refinement).''' If $(X,A)$ is a pair and $\gamma$ is an open cover of $X$, then the chain map generated by the [[inclusion]] of the sum of sub
  8 KB (1,367 words) - 13:49, 4 August 2013

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