# clique concept – Is the Rudin-Keisler ordering a steady relation? Answer

Hello pricey customer to our community We will proffer you an answer to this query clique concept – Is the Rudin-Keisler ordering a steady relation? ,and the respond will breathe typical via documented info sources, We welcome you and proffer you fresh questions and solutions, Many customer are questioning in regards to the respond to this query.

clique concept – Is the Rudin-Keisler ordering a steady relation?

If $$X, Y$$ are topological, and $$Rsubseteq Xtimes Y$$ we are saying that $$R$$ is steady (from $$X$$ to $$Y$$) if $$R^{-1}(V) = {uin U: exists vin V:(u,v)in R}$$ is launch in $$X$$.

Let $$textual content{NPU}(omega)$$ breathe the clique of non-principal ultafilters on $$omega$$. The Rudin-Keisler preorder on $$textual content{NPU}(omega)$$ is outlined by
$${cal U} leq_{RK} {cal V} :Leftrightarrow (exists f:omegatoomega)(forall Uin{cal U}) f^{-1}(U)in {cal V}$$ for $${cal U}, {cal V}in textual content{NPU}(omega)$$. It is simple to behold that $$leq_{RK}$$ is reflexive and transitive, however not anti-symmetric.

Let $$[omega]^omega$$ denote the gathering of innumerable subsets of $$omega$$. For $$Ain[omega]^omega$$, let $$u(A) = {{cal U}in textual content{NPU}(omega): Ain {cal U}}.$$ On $$textual content{NPU}(omega)$$ we deem the topology generated by the the gathering $${u(A): Ain[omega]^omega}$$.

Question. Is $$leq_{textual content{RK}}$$ a steady relation on $$textual content{NPU}(omega)$$ with this topology?

we are going to proffer you the answer to clique concept – Is the Rudin-Keisler ordering a steady relation? query through our community which brings all of the solutions from a number of dependable sources.