Ufyukyu

0 $begingroup$ Suppose $P$ and $Q subseteq P$ are posets, and let $tau$ and $rho$ be their respective Scott topologies. Now $Q$ is also equipped with the subspace topology $tauvert_Q$ inherited from $P$ . It is easy to see that: $$tauvert_Q subseteq rho$$ I have not found an example when the reverse inclusion is not also true. So my question is: When do the two topologies on $Q$ coincide? general-topology order-theory share | cite | improve this question edited Jan 22 at 9:55 Bernard Hurley asked Jan 22 at 9:13

0 $begingroup$ Let $V rightarrow M$ a vector bundle. $P rightarrow M$ a principal $G$ -bundle. Let $phi:G rightarrow GL(V)$ be a representation. A local section $s$ for $P$ , frame bundle for $V rightarrow M$ , defines an isomorphism $$psi_s: Omega^p(U) otimes Omega^0(V|_U) rightarrow Omega^p(U) otimes Omega^0(P times_G V|_U) $$ In this notation $Omega^0(underline{V}), $$Omega^0(P times_G V)$ de notes the sections of bundle. Hence, we have $p$ forms with values in this vector spaces respectively. I am confused, how is defined? EDIT: On second thought, I believe I have misunderstood the original question. We begin with a principal bundle $P rightarrow M$ , so $P$ is not the frame bundle of $V rightarrow M$ . Is this right? Then problem seems almost equivalent to Proposition 4.1, pa