Question

Y is convex set of x then order topology is same as subspace topology proof

Answer 1

Heyaaa...

Topology is same as subspace topology proof

Answer 2

Let X be an ordered set in the order topology, let Y be a subset of X that is convex in X. Then the order topology on Y is the same as the topology Y inherits as a subspace of X. ... Since the open rays of Y are a sub-basis for the order topology on Y , this topology is contained in the subspace topology.