G.A. Bliss, Algebraic Functions, American Mathematical Society Colloquium Publications xvi, New York 1933.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....means that for any parametrization (u, v) u(t) v(t) of f(u, v) 0, the t expansion of G(u(t) v(t) f v (u(t) v(t) contains no negative t powers. Using this fact in the parametrization u(t) t # , v(t) v i (t # This can be made explicit; see Notes See for example [2, 24]. and taking into account that du dt = i t # 1 , leads to the inequality ord t G(t # ) f v (t # ) # # i 1. Now on putting t # = u in the relation above we conclude that ord u f v (u, v i (u) # 1 For example, if f(u, v) 0 happens to be a Weierstrass equation to ....

G.A. Bliss, Algebraic Functions, American Mathematical Society Colloquium Publications xvi, New York 1933.

....[12, 13, 4] We will begin by reviewing the results of [13] 1.1 Review of Linear Topology It is well known that VEC, the category of vector spaces, is autonomous, i.e. symmetric monoidal closed. To obtain a autonomous category of vector spaces, we add a topological structure, due to Lefschetz [26]. Definition 1.1 Let V be a vector space. A topology, on V is linear if it satisfies the following three properties: ffl Addition and scalar multiplication are continuous, when the field k is given the discrete topology. ffl is hausdorff ffl 0 2 V has a neighborhood basis of open linear ....

S. Lefschetz, Algebraic Topology, American Mathematical Society Colloquium Publications 27, (1963).

.... the degree of the induced map from a small (n Gamma 2) sphere about p in X to the unit (n Gamma 2) sphere in the normal plane to the antidiagonal e Delta in S n Gamma1 Theta S n Gamma1 at (ff 0 ; ff 1 ) p) Replacing ff 0 by Gammaff 0 we recover the classical Lefschetz Coincidence Theorem [L] for maps into spheres: 7.28) Deg(ff 1 ) Gamma1) n Deg(ff 0 ) # points where ff 0 and ff 1 coincide. More generally Theorem 7.17 can be interpreted as a local formulation of the Lefschetz Coincidence Theorem [L] for smooth sections of sphere bundles. Proof of Lemma 7.24. For most of ....

....ff 0 by Gammaff 0 we recover the classical Lefschetz Coincidence Theorem [L] for maps into spheres: 7.28) Deg(ff 1 ) Gamma1) n Deg(ff 0 ) # points where ff 0 and ff 1 coincide. More generally Theorem 7. 17 can be interpreted as a local formulation of the Lefschetz Coincidence Theorem [L] for smooth sections of sphere bundles. Proof of Lemma 7.24. For most of the proof we work on the complement of the closed set Z = Zero(ff 0 ) Zero(ff 1 ) in X. First recall that the current e R defined via Condition B is given by e R = 0; 1) Div(fl) where (0; 1) denotes the characteristic ....

S. Lefschetz, Algebraic Topology, American Mathematical Society Colloquium Publications 27 (1942), Amer. Math. Soc., Providence R.I..

....the category has biproducts acting as tensor and par, then it is not hard to show that all ( nite) biproducts of the unit will also be in the core. This may then be a non trivial category. An example of this phenomenon is given by the category RTVec of re exive linear topological vector spaces [L63,Ba76,BS96], i.e. vector spaces equipped with a linear topology which are isomorphic to their double duals. In this category, all nite dimensional vector spaces are in the core but in nite dimensional vector spaces are not in the core. ii) As another example, consider the category of sup lattices, where ....

S. Lefschetz Algebraic Topology. American Mathematical Society Colloquium Publications 27, 1963.

....In our example, the dualizing object will be the base field. In an arbitrary symmetric monoidal closed category, objects for which is an isomorphism are called reflexive, or more precisely reflexive with respect to . 5. 1 Linear Topology The approach we use goes back to the work of Lefschetz [31], and has been studied by Barr [6] and the first author [10] The idea is to add to the linear structure an additional topological structure, and then define the dual space to be the linear continuous maps. This serves to decrease the size of the dual space and thus create a large class of ....

S. Lefschetz, Algebraic Topology, American Mathematical Society Colloquium Publications 27, (1963).

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC