Finding AC equivalent seen between two nodes of a BJT Amplifier
Looking from the emitter terminal, collector is a current source whose current cannot be changed. It offers infinite resistance and acts as an open circuit:  

\$R = \dfrac{\Delta V}{\Delta I} = \dfrac{\Delta V}{ 0} = \infty\$

Thus \$R_C\$ doesn't affect the impedance seen from emitter side.



You can obtain the resistance of a block by measuring the voltage and current. Suppose you put a current source \$i\$ at the emitter terminal. The voltage developed across the current source will be \$ir_e + \dfrac{i}{\beta}(R_1\| R_2)\$. Divide by the current to get the resistance seen at the emitter terminal.

Here \$r_e\$ is the resistane of transistor's base emitter junction.