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On Two Problems Relating to Liner Connected Topological Spaces


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1 Andhra University, India
     

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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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  • On Two Problems Relating to Liner Connected Topological Spaces

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Authors

T. Vijayaraghavan
Andhra University, India

Abstract


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?.