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de Rham cohomology
... We have dB (f (a)) = f (dA (a)) = f (0) = 0, since a ∈ Ker(dA ). Then f (a) ∈ Ker(dB ). Thus we set f ∗ : H p (A) −→ H p (B) by f ∗ ([a]) = [f (a)]. We must show that f ∗ is well defined. Let a0 ∈ Ker(dA ) such that [a] = [a0 ]. Then a − a0 = dA (x), where a ∈ Ap−1 . We have f (a0 ) − f (a) = f (a0 ...
... We have dB (f (a)) = f (dA (a)) = f (0) = 0, since a ∈ Ker(dA ). Then f (a) ∈ Ker(dB ). Thus we set f ∗ : H p (A) −→ H p (B) by f ∗ ([a]) = [f (a)]. We must show that f ∗ is well defined. Let a0 ∈ Ker(dA ) such that [a] = [a0 ]. Then a − a0 = dA (x), where a ∈ Ap−1 . We have f (a0 ) − f (a) = f (a0 ...
65, 3 (2013), 419–424 September 2013 TOTALLY BOUNDED ENDOMORPHISMS ON A TOPOLOGICAL RING
... Now, we start our main work with this observation that each class of totally bounded endomorphisms on a topological ring X, with respect to the topology of uniform convergence on bounded sets , is a closed subring of the ring of all endomorphisms on X, as shown by the following propositions. Proposi ...
... Now, we start our main work with this observation that each class of totally bounded endomorphisms on a topological ring X, with respect to the topology of uniform convergence on bounded sets , is a closed subring of the ring of all endomorphisms on X, as shown by the following propositions. Proposi ...
Stability and computation of topological invariants of solids in Rn
... is that lfs vanishes on the boundary of non-smooth objects. Theorems involving lfs do not help on non-smooth objetcs, such as solids with sharp edges. Fortunately, algorithms proved correct in the case of smooth objects, behave relatively well in practice on solids with sharp edges. In [7, 8], the a ...
... is that lfs vanishes on the boundary of non-smooth objects. Theorems involving lfs do not help on non-smooth objetcs, such as solids with sharp edges. Fortunately, algorithms proved correct in the case of smooth objects, behave relatively well in practice on solids with sharp edges. In [7, 8], the a ...
flows - IHES
... This paper carries over to flows results previously obtained for diffeomorphisms with regard to equilibrium states [6, 7, 24] and attractors [24]. For Anosov flows (A = M) the measure ~% has been studied in [9, 16, 17, 20, 25, 26-] and the theory of Gibbs states (a slightly different formalism from ...
... This paper carries over to flows results previously obtained for diffeomorphisms with regard to equilibrium states [6, 7, 24] and attractors [24]. For Anosov flows (A = M) the measure ~% has been studied in [9, 16, 17, 20, 25, 26-] and the theory of Gibbs states (a slightly different formalism from ...