592 Note in particular that when $k=1$ this implies a $C_*(\Homeo(I))$ action on $A$.

   592 Note in particular that when $k=1$ this implies a $C_*(\Homeo(I))$ action on $A$.

   593 (Compare with Example \ref{ex:e-n-alg} and the discussion which precedes it.)

   593 (Compare with Example \ref{ex:e-n-alg} and the discussion which precedes it.)

   594 Given a non-standard interval $J$, we define $\cC(J)$ to be

   594 Given a non-standard interval $J$, we define $\cC(J)$ to be

   595 $(\Homeo(I\to J) \times A)/\Homeo(I\to I)$,

   595 $(\Homeo(I\to J) \times A)/\Homeo(I\to I)$,

   596 where $\beta \in \Homeo(I\to I)$ acts via $(f, a) \mapsto (f\circ \beta\inv, \beta_*(a))$.

   596 where $\beta \in \Homeo(I\to I)$ acts via $(f, a) \mapsto (f\circ \beta\inv, \beta_*(a))$.

   598 Note that $\cC(J) \cong A$ (non-canonically) for all intervals $J$.

   597 Note that $\cC(J) \cong A$ (non-canonically) for all intervals $J$.

   599 We define a $\Homeo(J)$ action on $\cC(J)$ via $g_*(f, a) = (g\circ f, a)$.

   598 We define a $\Homeo(J)$ action on $\cC(J)$ via $g_*(f, a) = (g\circ f, a)$.

   600 The $C_*(\Homeo(J))$ action is defined similarly.

   599 The $C_*(\Homeo(J))$ action is defined similarly.

   601 

   600 

   602 Let $J_1$ and $J_2$ be intervals.

   601 Let $J_1$ and $J_2$ be intervals.