Multiplication of weak equivalence classes may be discontinuous

Weak Equivalence Classes of Complex Vector Bundles

For any complex vector bundle Ek of rank k over a manifold Mm with Chern classes ci ∈ H2i(Mm, Z) and any non-negative integers l1, · · · , lk we show the existence of a positive number p(m, k) and the existence of a complex vector bundle Êk over Mm whose Chern classes are p(m, k) · li · ci ∈ H2i(Mm, Z). We also discuss a version of this statement for holomorphic vector bundles over projective a...

The graph of equivalence classes and Isoclinism of groups

‎Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$‎. ‎In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$‎, ‎where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$‎. ‎We introduce a new graph determined ...

Some equivalence classes of operators on B(H)

You May be Able to Teach Early Classes, but Students May Not be Awake Yet!

Academic success of first-year students is one of the primary concerns of higher education institutes. A factor that may influence students’ success in a course and has been ignored is the effect of time of class on students’ performance. The goal of this study is to investigate the relationship between class time and students’ performance in a course to verify whether or not students enrolled ...

Topological Equivalence of Discontinuous Norms

We show that for every p > 0 there is an autohomeomorphism h of the countable infinite product of lines R N such that for every r > 0, h maps the Hilbert cube [ r , r ] N precisely onto the "elliptic cube" o~ {X ~ R N : ~ i = l I xi]p ~rP)" T h i s m e a n s that the supremum n o r m and, for instance, the Hilbert norm (p ---2) are topologically indistinguishable as functions on R N. The result...