Assignment:
Let X and Y connected, locally path connected and Hausdorff. let X be compact.
Let f: X ---> Y be a local homeomorphism. Prove that f is a surjective covering with finite fibers.
Prove:
a) Any subspace of a weak Hausdorff space is weak Hausdorff.
b) Any open subset U of a compactly generated space X is compactly generated if each point has an open neighborhood in X with closure contained in U.
c) Show that a space is Tychonoff iff it can be embedded in a cube.
d) There are Tychonoff spaces that are not k-spaces, but every cube is a compact Hausdorff space.
Provide complete and step by step solution for the question and show calculations and use formulas.