Number of species - genus

Japanese: 種数 - しゅすう（英語表記）genus

The surface of a lump of clay is homeomorphic to a sphere, but if you put your fingers through it to make n holes in it (Figure 1), the surface becomes homeomorphic to a surface made up of n connected lifebuoy-shaped surfaces (toruses) (Figure 2). A closed surface that can be oriented is homeomorphic to either a sphere or one of these surfaces, but if the number of holes is different, the surface will not be homeomorphic. In this way, the number of holes is an important number that completely classifies a closed surface that can be oriented topologically, and is called the genus, or genus of a closed surface that can be oriented.

Source: Heibonsha World Encyclopedia, 2nd Edition Information

Japanese:

粘土の塊の表面は球面と同相であるが，それに指を通してn個の穴を開ければ(図1)，その表面は浮輪の形をした曲面(トーラス)をn個連結した曲面(図2)と同相になる。向きがつけられる閉曲面は球面かまたはこれらの曲面のいずれかに同相で，穴の個数が異なれば同相にならない。このように穴の個数は，向きがつけられる閉曲面を位相的に完全に分類するたいせつな数で，向きがつけられる閉曲面の種数，または示性数と呼ばれている。

出典　株式会社平凡社世界大百科事典第２版について　情報

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