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在据一种href="//www.parkandroid.com/wiki/general-topology/" class="wiki_link" title="一般拓扑GydF4y2Ba" target="_blank">一般拓扑据/a>, 一种据strong>同性恋者据/strong>是保留所有拓扑属性的空间之间的地图。直观地,给定某种几何对象,a据em>拓扑财产据/em>是在物体在某种程度上拉伸或变形后保持不变的物体的属性。据/p>
例如,一个空间据span class="katex">
S.据/span>叫做据em>路径连接据/em>如果有两点据span class="katex">
S.据/span>可以加入a据一种href="//www.parkandroid.com/wiki/continuity-in-topology/?wiki_title=continuous" class="wiki_link new" title="连续GydF4y2Ba" target="_blank" rel="nofollow">连续据/a>曲线。在符号中,路径连接需要任何据span class="katex">
X据/span>那据span class="katex">
y据/span>∈据/span>S.据/span>,有一个连续的功能据span class="katex">
γ.据/span>:据/span>[据/span>0.据/span>那据/span>1据/span>]据/span>→据/span>S.据/span>这样据span class="katex">
γ.据/span>(据/span>0.据/span>)据/span>=据/span>X据/span>和据span class="katex">
γ.据/span>(据/span>1据/span>)据/span>=据/span>y据/span>。路径连接应被视为拓扑性质,因为拉伸据span class="katex">
S.据/span>只是拉伸据span class="katex">
γ.据/span>同样,问题的两点将通过新的拉伸空间中的一条路径保持联系。据/p>
正式地,两个之间的同胚据一种href="//www.parkandroid.com/wiki/topology/" class="wiki_link" title="拓扑空间GydF4y2Ba" target="_blank">拓扑空间据/a>
一种据/span>和据span class="katex">
B.据/span>是A.据一种href="//www.parkandroid.com/wiki/bijective-functions/" class="wiki_link" title="biGydF4y2Ba" target="_blank">bi据/a>
F据/span>:据/span>一种据/span>→据/span>B.据/span>这样据span class="katex">
F据/span>是连续的据span class="katex">
F据/span>-据/span>1据/span>:据/span>B.据/span>→据/span>一种据/span>也是连续的。然后,拓扑属性是据em>定义据/em>成为在OrchOmorphism中保存的拓扑空间的那些性质。回想一下,连续地图基本上是那些在域中发送彼此接近的点以在Codomain中彼此接近彼此接近的点。据/p>
对于任何一个据span class="katex">
一种据/span>据据/span>B.据/span>,开放间隔据span class="katex">
(据/span>一种据/span>那据/span>B.据/span>)据/span>⊂据/span>R.据/span>是ouromorphic to据span class="katex">
R.据/span>。据/p>
要展示这一点,请先注意据span class="katex">
(据/span>一种据/span>那据/span>B.据/span>)据/span>是ouromorphic to据span class="katex">
(据/span>0.据/span>那据/span>1据/span>)据/span>通过地图据span class="katex">
X据/span>↦据/span>(据/span>B.据/span>-据/span>一种据/span>)据/span>(据/span>X据/span>-据/span>一种据/span>)据/span>。这是一个同构族,因为它是一个持续的双重,其逆,据span class="katex">
X据/span>↦据/span>(据/span>B.据/span>-据/span>一种据/span>)据/span>X据/span>+据/span>一种据/span>,也是连续的。据/p>
因此,表现出同源族态度就足够了据span class="katex">
(据/span>0.据/span>那据/span>1据/span>)据/span>→据/span>R.据/span>。地图据span class="katex">
F据/span>:据/span>(据/span>0.据/span>那据/span>1据/span>)据/span>→据/span>R.据/span>给予据span class="katex-display">
F据/span>(据/span>X据/span>)据/span>=据/span>晒黑据/span>(据/span>π据/span>X据/span>-据/span>2据/span>π据/span>)据/span>会做这个诀窍,因为它是一个持续的双重,其逆,据span class="katex">
X据/span>↦据/span>π据/span>1据/span>(据/span>arctan.据/span>(据/span>X据/span>)据/span>+据/span>2据/span>π据/span>)据/span>,也是连续的。据/p>
立体投影是飞机之间的重要同源性据span class="katex">
R.据/span>2据/span>和据span class="katex">
2据/span>- 歇勒减去一个点。这据span class="katex">
2据/span>-领域据span class="katex">
S.据/span>2据/span>是一组积分据span class="katex">
(据/span>X据/span>那据/span>y据/span>那据/span>Z.据/span>)据/span>∈据/span>R.据/span>3.据/span>这样据span class="katex">
X据/span>2据/span>+据/span>y据/span>2据/span>+据/span>Z.据/span>2据/span>=据/span>1据/span>。让据span class="katex">
S.据/span>2据/span>∖据/span>{据/span>N据/span>}据/span>表示据span class="katex">
2据/span>- 歇勒减去北极,即点据span class="katex">
(据/span>0.据/span>那据/span>0.据/span>那据/span>1据/span>)据/span>。据/p>
存在一个同源形态据span class="katex">
F据/span>:据/span>S.据/span>2据/span>∖据/span>{据/span>N据/span>}据/span>→据/span>R.据/span>2据/span>,这可以描述如下。首先,确定集合据span class="katex">
P.据/span>=据/span>{据/span>(据/span>X据/span>那据/span>y据/span>那据/span>Z.据/span>)据/span>∈据/span>R.据/span>:据/span>Z.据/span>=据/span>0.据/span>}据/span>和据span class="katex">
R.据/span>2据/span>;地图据span class="katex">
P.据/span>→据/span>R.据/span>2据/span>给予据span class="katex">
(据/span>X据/span>那据/span>y据/span>那据/span>0.据/span>)据/span>↦据/span>(据/span>X据/span>那据/span>y据/span>)据/span>是一个同心的态度。据/p>
一个点据span class="katex">
P.据/span>∈据/span>S.据/span>2据/span>∖据/span>{据/span>N据/span>}据/span>, 让据span class="katex">
F据/span>(据/span>P.据/span>)据/span>表示独特的点据span class="katex">
P.据/span>这样的部分据span class="katex">
N据/span>F据/span>(据/span>P.据/span>)据/span>和据span class="katex">
S.据/span>2据/span>是据span class="katex">
P.据/span>。在坐标中,这张地图是精确的据span class="katex-display">
F据/span>(据/span>X据/span>那据/span>y据/span>那据/span>Z.据/span>)据/span>=据/span>(据/span>1据/span>-据/span>Z.据/span>X据/span>那据/span>1据/span>-据/span>Z.据/span>y据/span>)据/span>。据/span>
通过类似地定义的地图,人们可以显示据span class="katex">
N据/span>- 歇勒减去一个点据span class="katex">
(据/span>IE。,据span class="katex">
S.据/span>N据/span>∖据/span>{据/span>N据/span>}据/span>)据/span>是ouromorphic to据span class="katex">
R.据/span>N据/span>。据/p>
让据span class="katex">
F据/span>+据/span>:据/span>S.据/span>2据/span>-据/span>{据/span>N据/span>}据/span>→据/span>R.据/span>2据/span>从北极表示立体投影据span class="katex">
S.据/span>2据/span>,如Wiki HomeOmorphism所定义。同样,让我们据span class="katex">
F据/span>-据/span>:据/span>S.据/span>2据/span>-据/span>{据/span>S.据/span>}据/span>→据/span>R.据/span>2据/span>从南极表示立体投影据span class="katex">
S.据/span>2据/span>,即从该点开始据span class="katex">
S.据/span>=据/span>(据/span>0.据/span>那据/span>0.据/span>那据/span>-据/span>1据/span>)据/span>。据/p>
在据span class="katex">
R.据/span>2据/span>, 功能据span class="katex">
G据/span>:据/span>=据/span>F据/span>+据/span>∘据/span>F据/span>-据/span>-据/span>1据/span>明确定义。如果据span class="katex">
G据/span>(据/span>3.据/span>那据/span>4.据/span>)据/span>=据/span>(据/span>一种据/span>那据/span>B.据/span>)据/span>, 什么是据span class="katex">
一种据/span>+据/span>B.据/span>还是据/p>
2据/span>5.据/span>6.据/span>
2据/span>5.据/span>7.据/span>
2据/span>5.据/span>8.据/span>
2据/span>5.据/span>9.据/span>
笛卡尔岛据span class="katex">
R.据/span>2据/span>对真正的线没有祖美据span class="katex">
R.据/span>1据/span>。这可以通过矛盾来证明。据/p>
假设有一个同构族据span class="katex">
F据/span>:据/span>R.据/span>2据/span>→据/span>R.据/span>。选择据span class="katex">
P.据/span>∈据/span>R.据/span>2据/span>,并考虑据span class="katex">
F据/span>(据/span>P.据/span>)据/span>∈据/span>R.据/span>。如果据span class="katex">
F据/span>那是一个同构族,然后据span class="katex">
F据/span>限制在同源术之间据span class="katex">
R.据/span>2据/span>∖据/span>{据/span>P.据/span>}据/span>和据span class="katex">
R.据/span>∖据/span>{据/span>F据/span>(据/span>P.据/span>)据/span>}据/span>。但据span class="katex">
R.据/span>2据/span>∖据/span>{据/span>P.据/span>}据/span>是路径连接的,而在据span class="katex">
R.据/span>∖据/span>{据/span>F据/span>(据/span>P.据/span>)据/span>}据/span>不是!因此,据span class="katex">
F据/span>不能成为同友的。据span class="katex">
□据/span> 让据span class="katex">
R.据/span>2据/span>∖据/span>问:据/span>2据/span>表示笛卡尔平面减去所有点坐标都是理性的点。同样,让我们据span class="katex">
R.据/span>∖据/span>问:据/span>表示不合理的数量。是空间据span class="katex">
R.据/span>2据/span>∖据/span>问:据/span>2据/span>和据span class="katex">
R.据/span>∖据/span>问:据/span>homeOmorphic?据/p>
不据/span>
是的据/span>
暗示据/strong>: 是据span class="katex">
R.据/span>2据/span>∖据/span>问:据/span>2据/span>路径连接?据/p>
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问题加载......据/p>
注意加载......据/p>
设置加载......据/p>