Algebraic Topology: A First CourseWorld Publishing Corporation, 1995 - 430 pages Introduces the important ideas of algebraic topology by emphasizing the relation of these ideas with other areas of mathematics. This title focuses on concrete problems in spaces with a few dimensions, introducing only as much algebraic machinery as necessary for the problems encountered. |
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Page 12
... contained in U , so that Green's theorem can be applied , and it follows from Lemma 1.11 that f ( P ) is equal to g ... contained in the region , and starshaped means that there is a point Po in the region such that for any point P in ...
... contained in U , so that Green's theorem can be applied , and it follows from Lemma 1.11 that f ( P ) is equal to g ... contained in the region , and starshaped means that there is a point Po in the region such that for any point P in ...
Page 372
... contained in any open set of the covering . From the fact that K is compact it follows that there is a limit point P ... contained in U. There must be ( in- finitely many ) n with 1 / n < r / 2 such that A , meets the open ball of radius ...
... contained in any open set of the covering . From the fact that K is compact it follows that there is a limit point P ... contained in U. There must be ( in- finitely many ) n with 1 / n < r / 2 such that A , meets the open ball of radius ...
Page 376
... contained in U1 , let σ2 be the sum of those among the others such that the closure of the support is contained in U2 , and continue in this way until all ha are used ; set the other σ , equal to zero . 1 α α Step 4. To complete the ...
... contained in U1 , let σ2 be the sum of those among the others such that the closure of the support is contained in U2 , and continue in this way until all ha are used ; set the other σ , equal to zero . 1 α α Step 4. To complete the ...
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Expressions et termes fréquents
1-cycle a₁ Algebraic analytic Aut(Y/X base point boundary Chapter circle closed 1-chain closed 1-form closed paths cohomology compact complement complex connected components constant path construct contained continuous mapping coordinate Corollary covering map define denoted determines diffeomorphic differential disk element endpoints equivalence exact Exercise fact follows formula free abelian group function f fundamental group G-covering group G H₁U H₁X homology group homomorphism homotopy identity map integral interval isomorphism Jordan curve theorem Lemma lifting locally constant locally constant function locally path-connected loop mapping f Mayer-Vietoris meromorphic neighborhood open set P₁ Problem Proof Proposition prove quotient rectangle restriction Rham Riemann surface semilocally simply connected sequence Show simply connected singularities sphere subgroup Suppose surjective t₁ takes theorem topology trivial U₁ unique universal covering vector field vector space winding number y₁ zero