Download A Basic Course in Algebraic Topology (Graduate Texts in by William S. Massey PDF

By William S. Massey

ISBN-10: 038797430X

ISBN-13: 9780387974309

"This ebook is meant to function a textbook for a direction in algebraic topology initially graduate point. the most issues coated are the category of compact 2-manifolds, the basic team, masking areas, singular homology conception, and singular cohomology conception. those issues are constructed systematically, fending off all pointless definitions, terminology, and technical equipment. anywhere attainable, the geometric motivation at the back of a number of the suggestions is emphasised. The textual content involves fabric from the 1st 5 chapters of the author's prior ebook, ALGEBRAIC TOPOLOGY: AN advent (GTM 56), including just about all of the now out-of-print SINGULAR HOMOLOGY concept (GTM 70). the cloth from the sooner books has been conscientiously revised, corrected, and taken as much as date."

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H = {0, 1, –1, 〈2Z ∪ 2I〉, i, –i}, H = proper subset of 〈G ∪ I〉 and 59 H = H1 ∪ H2 = {1 –1 i – i} ∪ {〈2Z ∪ 2I〉} is a neutrosophic subbigroup but H is not a group under ‘+’ or ‘o’. Thus we give a nice characterization theorem about the strong neutrosophic subbigroup. 3: Let {〈G ∪ I〉, +, o} be a strong neutrosophic bigroup. Then the subset H (≠ φ) is a strong neutrosophic subbigroup of 〈G ∪ I〉 if and only if there exists two proper subsets 〈G1 ∪ I〉, 〈G2 ∪ I〉 of 〈G ∪ I〉 such that i. ii. 〈G ∪ I〉 = 〈G1 ∪ I〉 ∪ 〈G2 ∪ I〉 with (〈G1 ∪ I〉, +) is a neutrosophic group and (〈G2 ∪ I〉, o) a neutrosophic group.

P is a neutrosophic subbigroup. o(P) = 7 and (7, 17) = 1. In fact order of none of the neutrosophic subbigroups will divide the order of the neutrosophic bigroup as o(BN(G)) = 17, a prime. 6: Let BN(G) = {B(G1) ∪ B(G2), *1, *2} where 55 B(G1) = B(G2) = {0, 1, 2, 3, 4, I, 2I, 3I, 4I, 1 + I, 2 + I, 3 + I, 4 + I, 1 + 2I, 2 + 2I, 3 + 2I, 4 + 2I, 1 + 3I, 2 + 3I, 3 + 3I, 4 + 3I, 4 + 4I, 3 + 4I, 2 + 4I, 1 + 4I } be a neutrosophic group under multiplication modulo 5. {g | g10 = 1} a cyclic group of order 10.

If both B(G1) and B(G2) are cyclic, we call BN(G) a cyclic bigroup. We wish to state the notion of normal bigroup. 4: Let BN (G) = {B(G1) ∪ B(G2), *1, *2} be a neutrosophic bigroup. P(G) = {P(G1) ∪ P(G2), *1, *2} be a neutrosophic bigroup. P(G) = {P(G1) ∪ P(G2), *1, *2} is said to be a neutrosophic normal subbigroup of BN(G) if P(G) is a neutrosophic subbigroup and both P(G1) and P(G2) are normal subgroups of B(G1) and B(G2) respectively. We just illustrate this by the following example. 4: BN(G) = {B(G1) ∪ B(G2), *1, *2}; where B(G1) = {1, 4, 2, 3, I, 2I 3I, 4I} and B(G2) = S3.

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