Abstract

We prove that a connected space X is a COTS with endpoints iff there is a one–one Darboux function from X onto a space with endpoints. Using this result, we show that a connected space X is homeomorphic to the closed unit interval if it is T1 separable and locally connected and there is a one–one Darboux function from X onto a space with endpoints. Also we obtain some other characterizations of COTS with endpoints and some characterizations of the closed unit interval.

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