To-iūⁿ-thé

To-iūⁿ-thé (manifold, liû-hêng) sī kā kán-tan ê khong-kan sió oan-khiau--chi̍t-ē koh liâm chò-hoé ê sò͘-ha̍k khong-kan. Khó-pí kóng kā 2 tiâu soàⁿ-koe̍h sió aú hō͘ oan koh kā in ê boé-liu liâm--khí-lâi tō ē pìⁿ-chiâⁿ 1 ê îⁿ. Nā kā 1 tiuⁿ tn̂g-ko-hêng ê choá ê 1 pêng seng tńg 180°, koh kap lēng-goā 1 pêng liâm chò-hoé, tō ē pìⁿ-chiâⁿ 1 ê Möbius îⁿ-toà. To-iūⁿ-thé siōng kài chán ê só͘-chāi tō sī ē-tit ēng khah kán-tan, khah liáu-kái ê khong-kan lâi taù. Ēng bô kāng khoán ê khong-kan chò sò͘-châi, ē-tàng taù bô kāng khoán ê to-iūⁿ-thé chhut--lâi, pí-lūn kóng ūi-siòng to-iūⁿ-thé (topological manifold), thang-bî to-iūⁿ-thé (differentiable manifold). To-iūⁿ-thé tī bu̍t-lí-ha̍k ê iōng-tô͘ chin toā, chhiūⁿ kóng kó͘-tián le̍k-ha̍k (classical mechanics) ê siòng khong-kan (phase space) kap kóng-gī siong-tùi-lūn (general relativity) ê sî-khong (spacetime) bô͘-hêng ēng--ê 4D ké Riemann to-iūⁿ-thé lóng sī thang-bî to-iūⁿ-thé.

Möbius îⁿ-toà