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In this paper, we study the prime filters of a bounded pseudocomplemented semilattice. We extend some of the results of \([3]\) to pseudocomplemented semilattices. It is observed that the set of all prime filters \( \mathcal{P} \) of a pseudocomplemented semilattice \( S \) is a topology, and it is \( T_0 \) and compact. We also obtain some necessary and sufficient conditions for the subspace of maximal filters to be normal.