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?.
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