On Two Problems Relating to Liner Connected Topological Spaces

In this note I answer two questions of Dr R. Vaidyanathaswamy.

The questions are

(i) Suppose that a connected linearly ordered topological space S has the power of the continuum; does it follow that S has an everywhere dense enumerable subset?

(ii) A point P of a connected topological space S is said to be a cut point if its removal splits S into two (and only two) disjoint connected open topological spaces. If every point P of a connected topological space S is a cut point of S does it imply then that S is a linear space?.