In the first months after the launch in July 2019, eROSITA onboard Spektr-RG (SRG) performed long-exposure observations in the regions around SN 1987A and SNR N132D in the Large Magellanic Cloud (LMC). We analyse the distribution and the spectrum of the diffuse X-ray emission in the observed fields to determine the physical properties of the hot phase of the interstellar medium (ISM). The eROSITA data are complemented by newly derived column density maps for the Milky Way and the LMC, 888 MHz radio continuum map from the Australian Square Kilometer Array Pathfinder (ASKAP), and optical images of the Magellanic Cloud Emission Line Survey (MCELS). We detect significant emission from thermal plasma with kT=0.2 keV in all the regions. There is also an additional higher-temperature emission component from a plasma with kT = 0.7 keV. In addition, non-thermal X-ray emission is significantly detected in the superbubble 30 Dor C. The absorbing column density NH in the LMC derived from the analysis of the X-ray spectra taken with eROSITA is consistent with the NH obtained from the emission of the cold medium over the entire area. Neon abundance is enhanced in the regions in and around 30 Dor and SN 1987A, indicating that the ISM has been chemically enriched by the young stellar population. Emission from the stellar cluster RMC 136 and the Wolf-Rayet stars RMC 139 and RMC 140 is best modelled with a high-temperature (kT>1 keV) non-equilibrium ionisation plasma emission and a non-thermal component with a photon index of {Gamma} =1.3. In addition, the optical SNR candidate J0529-7004 is also detected with eROSITA and we thus confirm the source as an SNR.
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