We report on X-ray observations of the core of the Shapley Supercluster. Combining data from pointed observations of the ROSAT PSPC detector and data from the ROSAT All-Sky Survey, the observed region covers an area of $6^\circ \times 3^\circ$. It contains the central clusters A3562, A3558 and A3556. We find clear evidence for X-ray emission connecting the three clusters. This confirms the existence of a filamentary, physical structure embedding the three clusters A3562, A3558 and A3556. We also find evidence for faint emission westwards of A3556. In total, the extension of the filamentary X-ray emission of the core of the Shapley Supercluster amounts up to at least $\sim 17.5 h_{50}^{-1}\sim 16\times10^{44} h_{50}^{-2}^{-1}$.

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