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A \emph{surface} is a two-dimensional topological manifold.
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A \emph{surface} is a two dimensional topological manifold.
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| A closed surface is a surface without boundary. |
A closed surface is a surface without boundary. |
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| A result called the "classification theorem" gives us a symbolic semantics, matching the geometrical view point, in terms of genera, orientability and number of boundary components. Together with the connected sum operation, they make available a powerful language to be explored and exploited. |
A result called the "classification theorem" gives us a symbolic semantics, matching the geometrical view point, in terms of genera, orientability and number of boundary components. Together with the connected sum operation, they make available a powerful language to be explored and exploited. |
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| As an example of a surface take $T=S^1\times S^1$ the two torus, the boundary of a solid sugar donut shaped cake $D^2\times S^1$, where $S^1$ is the familiar modulus one complex numbers. |
As an example of a surface take $T=S^1\times S^1$ the two torus, the boundary of a solid sugar donut shaped cake $D^2\times S^1$, where $S^1$ is the familiar modulus one complex numbers. |
