The structure you are describing sounds like the endoplasmic reticulum (ER), particularly the rough endoplasmic reticulum (RER) if ribosomes are present on its outer surface, or it could also refer to the smooth endoplasmic reticulum (SER) if no ribosomes are attached.
Biological Function:
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Rough Endoplasmic Reticulum (RER): The RER is primarily involved in the synthesis and processing of proteins. Ribosomes on its surface translate mRNA into polypeptide chains, which are then folded and modified within the lumen of the RER. It is also involved in the post-translational modification of proteins, such as glycosylation.
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Smooth Endoplasmic Reticulum (SER): The SER is involved in several metabolic processes, including lipid synthesis, detoxification of drugs and poisons, and calcium ion storage. It does not have ribosomes on its surface, which distinguishes it from the rough ER.
In summary, the net-like membranous complex you described is most likely the endoplasmic reticulum, and its primary functions involve protein and lipid synthesis, as well as other metabolic processes depending on whether it is rough or smooth.