# Semantic search

Connected and T1 with at least two points implies infinite, Connected not implies locally connected, Connected not implies path-connected, Connectedness is closure-preserved, Connectedness is connected union-closed, Connectedness is continuous image-closed, Connectedness is not box product-closed, Connectedness is not hereditary, Connectedness is not weakly hereditary, Connectedness is product-closed, Irreducible implies connected, Path-connected implies connected