# Are geometric conditions open?

Let $$k$$ be a field, $$X$$ and $$Y$$ be $$k$$-schemes, $$X\rightarrow Y$$ be a $$k$$-open immersion with dense image. Assume that $$Y$$ is an integral scheme. Suppose that:

• $$X$$ is geometrically connected, is $$Y$$ geometrically connected then?
• $$X$$ is geometrically reduced, is $$Y$$ geometrically reduced then?
• $$X$$ is geometrically integral, is $$Y$$ geometrically integral then?