Topology
Prove or disprove ( with a counterexample)
(a) The continuous image of a Hausdorff space is Hausdorff.
(b) The continuous image of a connected space is
connected.
Prove or disprove with a counterexample the next claims:
(a) The complement of a decidable language is decidable.
(b) The Kleene star of a Turing-recognizable language is
Turing-recognizable.