fundamental group การใช้

• It follows that the fundamental group of the pseudocircle is infinite cyclic.
• As a consequence, two homotopy equivalent path-connected spaces have isomorphic fundamental groups:
• However, the fundamental group " is " an important concept in mathematics.
• Their fundamental groups are isomorphic because each space is simply connected.
• Perhaps surprisingly, there are finite topological spaces with nontrivial fundamental groups.
• The area makes use of the connection of graphs via their fundamental groups.
• These results applied to the algebraic fundamental group and to the Picard group.
• The fundamental group of a rose is generator for each petal.
• The sphere is simply connected, while the real projective plane has fundamental group.
• The fundamental group is generated by loops winding around each arc.
• So these three-manifolds are completely determined by their fundamental group.
• The topological proof based on fundamental groups of bouquets of circles is due to.
• The fundamental group is either icosahedral group by a cyclic group of even order.
• Zariski had been working on the fundamental group of the presentation for the group.
• The fundamental group functor takes products and coproducts to coproducts.
• Free homotopy classes of free loops correspond to conjugacy classes in the fundamental group.
• In the case it is also called the fundamental group.
• The fundamental group of the unit circle is isomorphic to the group of integers.
• So there was a desire to generalise the nonabelian fundamental group to all dimensions.
• This is non-trivial in the fundamental group, and thus the Borromean rings are linked.