twisted free tensor products - American Mathematical Society
... correspondence from px.b.s to tf.p.s. The total space of a p.c.b. may have more than one representation as a t.f.p. 3. The construction of a twisted free tensor product. In this section we associate with every t.f.p. A * , FX, a differential graded algebra, which we call a twisted free tensor produc ...
... correspondence from px.b.s to tf.p.s. The total space of a p.c.b. may have more than one representation as a t.f.p. 3. The construction of a twisted free tensor product. In this section we associate with every t.f.p. A * , FX, a differential graded algebra, which we call a twisted free tensor produc ...
Remarks on neighborhood star-Lindel¨of spaces II
... is not neighborhood star-Lindelöf, since it is homeomorphic to S1 . Finally we show that X is neighborhood star-Lindelöf. We need only show that X is strongly starLindelöf, since every strongly star-Lindelöf space is neighborhood star-Lindelöf. To this end, let U be an open covers of X. Since φ ...
... is not neighborhood star-Lindelöf, since it is homeomorphic to S1 . Finally we show that X is neighborhood star-Lindelöf. We need only show that X is strongly starLindelöf, since every strongly star-Lindelöf space is neighborhood star-Lindelöf. To this end, let U be an open covers of X. Since φ ...
Generalized functions
... We first observe that if a topological vector space admits a continuous norm then the open convex set define as its unit ball does not contain a line. So, it will be enough to find a locally convex topological vector space such that every non empty open set contains a line. Consider Rω with the prod ...
... We first observe that if a topological vector space admits a continuous norm then the open convex set define as its unit ball does not contain a line. So, it will be enough to find a locally convex topological vector space such that every non empty open set contains a line. Consider Rω with the prod ...
PRODUCTS OF PROTOPOLOGICAL GROUPS JULIE C. JONES
... 1. Introduction. Montgomery and Zippin [5] saied that a group is approximated by Lie groups if every neighborhood of the identity contains an invariant subgroup H such that G/H is topologically isomorphic to a Lie group. Using a similar idea, Bagley, Wu, and Yang [1] defined a pro-Lie group. Covingto ...
... 1. Introduction. Montgomery and Zippin [5] saied that a group is approximated by Lie groups if every neighborhood of the identity contains an invariant subgroup H such that G/H is topologically isomorphic to a Lie group. Using a similar idea, Bagley, Wu, and Yang [1] defined a pro-Lie group. Covingto ...
Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below. In this case, C is called a covering space and X the base space of the covering projection. The definition implies that every covering map is a local homeomorphism.Covering spaces play an important role in homotopy theory, harmonic analysis, Riemannian geometry and differential topology. In Riemannian geometry for example, ramification is a generalization of the notion of covering maps. Covering spaces are also deeply intertwined with the study of homotopy groups and, in particular, the fundamental group. An important application comes from the result that, if X is a ""sufficiently good"" topological space, there is a bijection between the collection of all isomorphism classes of connected coverings of X and the conjugacy classes of subgroups of the fundamental group of X.