SIFAT-SIFAT MANIFOLD TOPOLOGI
DOI:
https://doi.org/10.25077/jmu.7.2.1-9.2018Abstract
Abstrak. Manifold topologi merupakan ruang topologi dengan sifat-sifat tertentu yangmenggambarkan bahwa ruang tersebut secara lokal terlihat seperti Rn. Topologi meru-
pakan kajian objek geometri yang
eksibel dengan mengawetkan proses deformasi objek
yang diawetkan oleh homeomorsma. Manifold topologi adalah suatu generalisasi dari
kurva dan permukaan. Penelitian ini bertujuan untuk mengkaji manifold topologi pada
ruang Euklidis Rn yang memiliki sifat-sifat Hausdor, mempunyai countable basis dan
Euklidis berdimensi n lokal dan manifold topologi dengan smooth structure. Penelitian
ini juga mengkaji bahwa grak dari f yang didenisikan oleh
ô€€€(f) = f(x; y) 2 Rn Rkj x 2 U dan y = f(x)g;
dengan topologi subruang dari Rn+k adalah suatu manifold topologi berdimensi n, jika
U Rn adalah buka dan f : U ! Rk adalah kontinu. Selanjutnya dibahas bahwa grak
ô€€€(f) adalah manifold smooth apabila ditambahkan smooth structure ' : ô€€€(f) ! U.
Kata Kunci: Ruang Euklidis, Manifold Topologi, Hausdor, Countable Basis, Smooth
Structure, Homeomorsma, Grak Fungsi, Chart, Manifold Smooth
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