Uniform maps into normed spaces
... concludes the proof. The last set of characterizations is given in the concluding. THEOREM 4. - Each of the following conditions (11) - (13) is equivalent to the conditions ( 1 ) — ( 1 0 ) : 11) For any normed space B, the linear space U(X , B) is scalar inversion-closed, i.e. if f : X -> B G U does ...
... concludes the proof. The last set of characterizations is given in the concluding. THEOREM 4. - Each of the following conditions (11) - (13) is equivalent to the conditions ( 1 ) — ( 1 0 ) : 11) For any normed space B, the linear space U(X , B) is scalar inversion-closed, i.e. if f : X -> B G U does ...
COMBINATORIAL HOMOTOPY. I 1. Introduction. This is the first of a
... of the homotopy type of any 3-dimensional complex (see [3]) and of any finite, simply-connected, 4-dimensional complex. An account of the former will be given in Paper II of this series and of the latter in [S]. This and Theorem 6 below lead to an algebraic description of the 3-type of any complex a ...
... of the homotopy type of any 3-dimensional complex (see [3]) and of any finite, simply-connected, 4-dimensional complex. An account of the former will be given in Paper II of this series and of the latter in [S]. This and Theorem 6 below lead to an algebraic description of the 3-type of any complex a ...
NEW TYPES OF COMPLETENESS IN METRIC SPACES
... Next, we generate another class of sequences which are cofinal with respect to the previous ones, in the sense that the residuality of the indexes is replaced by the cofinality. Then, we obtain what we call cofinally Bourbaki–Cauchy sequences. Recall that the corresponding cofinal notion associated to t ...
... Next, we generate another class of sequences which are cofinal with respect to the previous ones, in the sense that the residuality of the indexes is replaced by the cofinality. Then, we obtain what we call cofinally Bourbaki–Cauchy sequences. Recall that the corresponding cofinal notion associated to t ...
SOFT TOPOLOGICAL QUESTIONS AND ANSWERS M. Matejdes
... on F(A, X) stated in Definition 2.1 or by the corresponding relation operations. For example ⊔t∈T (Gt , A) = (∪t∈T Gt , A) = (F∪t∈T RGt , A). From the one-to-one correspondence between the relations from R(A, X) and the set valued mappings from F(A, X), a soft topological space can be characterizes ...
... on F(A, X) stated in Definition 2.1 or by the corresponding relation operations. For example ⊔t∈T (Gt , A) = (∪t∈T Gt , A) = (F∪t∈T RGt , A). From the one-to-one correspondence between the relations from R(A, X) and the set valued mappings from F(A, X), a soft topological space can be characterizes ...
EXISTENCE AND PROPERTIES OF GEOMETRIC QUOTIENTS
... Deligne has proved the existence of geometric quotients of separated algebraic spaces by arbitrary actions of finite discrete groups, but without any published proof, cf. [Knu71, p.183]. Deligne’s idea was to use fix-point reflecting étale covers to deduce the existence from the affine case. Kollá ...
... Deligne has proved the existence of geometric quotients of separated algebraic spaces by arbitrary actions of finite discrete groups, but without any published proof, cf. [Knu71, p.183]. Deligne’s idea was to use fix-point reflecting étale covers to deduce the existence from the affine case. Kollá ...
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.