The structure that encloses the nucleus is called the nuclear envelope.

Here's a breakdown:

* Nuclear envelope: A double membrane that surrounds the nucleus and separates it from the cytoplasm. It's composed of two lipid bilayers with a space called the perinuclear space between them.

* Function: The nuclear envelope controls what enters and exits the nucleus, protecting the DNA and regulating gene expression. It also provides structural support for the nucleus.

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