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In this article we are concern for the following Choquard equation \[ -\Delta u = \lambda |u|^{q-2}u +\left(\int_\Omega \frac{|u(y)|^{2^*_\mu}}{|x-y|^\mu} dy \right)|u|^{2^*_\mu-2} u \; \text{in}\; \Omega,\quad u = 0 \; \text{ on } \partial \Omega , \] where $\Omega$ is an open bounded set with continuous boundary in $\mathbb{R}^N( N\geq 3)$, $2^*_{\mu}=\frac{2N-\mu}{N-2}$ and $q \in [2,2^*)$ where $2^*=\frac{2N}{N-2}$. Using Lusternik-Schnirelman theory, we associate the number of positive solutions of the above problem with the topology of $\Omega$. Indeed, we prove if $\lambda 3 $ or $4

The effect of topology on the number of positive solutions of elliptic equation involving Hardy-Littlewood-Sobolev critical exponent