A continuous path of singular masas in the hyperfinite II1factor

摘要: Using methods of R.J.Tauer we exhibit an uncountable family singular masas in the hyperfinite $\textrm{II}_1$ factor $\R$ all with Puk\'anszky invariant $\{1\}$, no pair which are conjugate by automorphism $R$. This is done introducing $\Gamma(A)$ for a masa $A$ \IIi $N$ as maximal size projection $e\in A$ $A e$ contains non-trivial centralising sequences $eN e$. The produced give rise to continuous map from interval $[0,1]$ into equiped $d_{\infty,2}$-metric. A result also given showing that $d_{\infty,2}$-upper semi-continuous. As consequence, sets $\{n\}$ closed.