GRUP HOMOLOGI YANG TEREDUKSI PADA HIMPUNAN KUBIK
DOI:
https://doi.org/10.25077/jmu.3.4.66-69.2014Abstract
Diberikan suatu ruang topologi X. Selanjutnya didefinisikan suatu objek aljabar H∗ (X) yang disebut dengan homologi dari X dan (H˜∗ (X)) yang disebut dengan homologi yang tereduksi dari X. Himpunan grup homologi ke-k dari X dinotasikan dengan Hk(X) dan (H˜k(X)) merupakan himpunan grup homologi ke-k yangtereduksi dari X. H0(X) merupakan grup homologi berdimensi nol yang menyatakan
banyaknya connected component pada himpunan kubik tersebut, dimana himpunan
titik-titik pada {Pi|i = 1, · · · ,n} pada X terdiri atas satu titik dari masing-masing
connected component pada X. Pada skripsi ini, dikaji bahwa Hk(X) isomorfik dengan
(H˜k(X)) dimana k 6= 0. Koleksi dari rantai dasar [Pˆ i − Pˆ 0] ∼ yang bersesuaian dengan
Pi ({[Pi − P0] ∼ ∈ H˜ 0(X) | i = 1,...,n}) membentuk suatu basis untuk (H˜ 0(X)).
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