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      <title>Thomas Second Brain</title>
      <link>https://obvault.thomas-hub.com</link>
      <description>Last 10 notes on Thomas Second Brain</description>
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    <title>MaxFlow Problem</title>
    <link>https://obvault.thomas-hub.com/Programming/Algorithms--and--Probability-ETH/MaxFlow-Problem</link>
    <guid>https://obvault.thomas-hub.com/Programming/Algorithms--and--Probability-ETH/MaxFlow-Problem</guid>
    <description><![CDATA[  Problem Given a network N=(V,A,c,s,t), find the flow f with the greatest value Definition - cut A cut in the network is a partition of the vertex set V into two disjoint subsets S and T such that s \in S, t \in T The capacity of a cut (S, T) is the total capacity of all edges from S to T: c(S, T) \... ]]></description>
    <pubDate>Sat, 09 May 2026 18:14:22 GMT</pubDate>
  </item><item>
    <title>Cell Complex</title>
    <link>https://obvault.thomas-hub.com/Math/Algebraic-Topology/Cell-Complex</link>
    <guid>https://obvault.thomas-hub.com/Math/Algebraic-Topology/Cell-Complex</guid>
    <description><![CDATA[ Notation e^{n} is an n cell, homeomorphic to the open n disk D^{n}-\partial D^{n} or D^{n}-S^{n-1} or Int(D^{n}) Construction We start from a discrete set X^{0} (0-cells) form the n-skeleton X^{n} from X^{n-1} by attaching n-cells e^{n} via the attaching map \varphi _{\alpha}:S^{n-1}\to X^{n-1} For ... ]]></description>
    <pubDate>Sat, 09 May 2026 17:54:29 GMT</pubDate>
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    <title>Covering Space</title>
    <link>https://obvault.thomas-hub.com/Math/Algebraic-Topology/Covering-Space</link>
    <guid>https://obvault.thomas-hub.com/Math/Algebraic-Topology/Covering-Space</guid>
    <description><![CDATA[ Definition Given a space X, a covering space of X consists of a space \tilde{X} and a map p : \tilde{X} \to X satisfying the following condition: For each point x \in X there is an open neighborhood U of x in X such that p^{-1}(U) is a union of disjoint open sets each of which is mapped homeomorphic... ]]></description>
    <pubDate>Sat, 09 May 2026 16:58:43 GMT</pubDate>
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    <title>Fundamental Group</title>
    <link>https://obvault.thomas-hub.com/Math/Algebraic-Topology/Fundamental-Group</link>
    <guid>https://obvault.thomas-hub.com/Math/Algebraic-Topology/Fundamental-Group</guid>
    <description><![CDATA[ Definition If the starting and ending point of a path are the same, then this path is called a loop The common starting and ending point x_{0} is referred to as the basepoint The set of all homotopy classes [f] of loops f:I\to X at the basepoint x_{0} is denoted \pi_{1}(X,x_{0}) Proposition 1.3 ( Al... ]]></description>
    <pubDate>Sat, 09 May 2026 16:51:00 GMT</pubDate>
  </item><item>
    <title>Homotopy</title>
    <link>https://obvault.thomas-hub.com/Math/Algebraic-Topology/Homotopy</link>
    <guid>https://obvault.thomas-hub.com/Math/Algebraic-Topology/Homotopy</guid>
    <description><![CDATA[ Formal Definition A Homotopy is a continuous deformation between two continuous maps. Let f,g:X\to Y be continuous maps. ]]></description>
    <pubDate>Sat, 09 May 2026 00:03:10 GMT</pubDate>
  </item><item>
    <title>Clever Homotopy Equivalences</title>
    <link>https://obvault.thomas-hub.com/Math/Algebraic-Topology/Clever-Homotopy-Equivalences</link>
    <guid>https://obvault.thomas-hub.com/Math/Algebraic-Topology/Clever-Homotopy-Equivalences</guid>
    <description><![CDATA[  ]]></description>
    <pubDate>Sat, 09 May 2026 00:00:43 GMT</pubDate>
  </item><item>
    <title>Path Connectedness</title>
    <link>https://obvault.thomas-hub.com/Math/Topology/Path-Connectedness</link>
    <guid>https://obvault.thomas-hub.com/Math/Topology/Path-Connectedness</guid>
    <description><![CDATA[ Definition - Path Let X be a topological space and p,q\in X. ]]></description>
    <pubDate>Fri, 08 May 2026 17:19:57 GMT</pubDate>
  </item><item>
    <title>Free Group</title>
    <link>https://obvault.thomas-hub.com/Math/Abstract-Algebra/Free-Group</link>
    <guid>https://obvault.thomas-hub.com/Math/Abstract-Algebra/Free-Group</guid>
    <description><![CDATA[ Definition Let S be a set of symbols. ]]></description>
    <pubDate>Fri, 08 May 2026 17:08:41 GMT</pubDate>
  </item><item>
    <title>Section 4 Groups</title>
    <link>https://obvault.thomas-hub.com/Math/Abstract-Algebra/Section-4-Groups</link>
    <guid>https://obvault.thomas-hub.com/Math/Abstract-Algebra/Section-4-Groups</guid>
    <description><![CDATA[ Group is a algebra structure: Transclude of Algebra-Structure.excalidraw Definition: Group - normal definition A group \langle G,*\rangle is a set G, with a operation *, such that the following axioms are satisfied: The set is closed under * associativity of * identity element e for * Every element ... ]]></description>
    <pubDate>Fri, 08 May 2026 16:56:05 GMT</pubDate>
  </item><item>
    <title>Relation</title>
    <link>https://obvault.thomas-hub.com/Math/Discrete-Mathematics-ETH/Relation</link>
    <guid>https://obvault.thomas-hub.com/Math/Discrete-Mathematics-ETH/Relation</guid>
    <description><![CDATA[  NOTE A relation is a special set Inverse of Relation Discrete Mathematics ETH, p.53 The inverse of a relation ρ from A to B is the relation \rho from B to A defined by \hat{\rho}\overset{ def }{ = }\{ (b,a)|(a,b)\in \rho \} Eigenschaften von Relation Eigenschaften von Relation \rho auf A: reflexiv:... ]]></description>
    <pubDate>Thu, 07 May 2026 20:29:21 GMT</pubDate>
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