In this work, 2-absorbing
![$ z$](img1.png)
-filters on a topological space
![$ X$](img2.png)
are defined and their general properties are examined. Moreover, the convergence of 2-absorbing
![$ z$](img1.png)
-filters is studied. A correspondence between 2-absorbing
![$ z$](img1.png)
-filters on
![$ X$](img2.png)
and 2-absorbing
![$ z$](img1.png)
-ideals of the ring
![$ C(X)$](img3.png)
of all real-valued continuous functions on
![$ X$](img2.png)
is given.