X is connected iff does not exist continuous surjective function from X to dicrete two point space

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X is connected iff there does X is connected iff there does't exist surjective cont function from X onto two point discrete space.
space is connected iff a continuous function from X to discrete space Y reduces to constant function space is connected iff a continuous function from X to discrete space Y reduces to constant function
X is connected iff every continuous function from X to discrete space D reduce to constant function. X is connected iff every continuous function from X to discrete space D reduce to constant function.
Set Topology| Connected spaces| Theorem no. 3 Set Topology| Connected spaces| Theorem no. 3
The Continuous Image of connected space is connected | Space is disconnected iff A is open & closed The Continuous Image of connected space is connected | Space is disconnected iff A is open & closed
Definition of a Surjective Function and a Function that is NOT Surjective Definition of a Surjective Function and a Function that is NOT Surjective
Connected Spaces|Connected subspace|Continuous image|Continuous surjective function|Limit points Connected Spaces|Connected subspace|Continuous image|Continuous surjective function|Limit points
Lec4.5:Thm4.1.7:(X,d) is connected iff the only continuous map of(X,d) onto(X0,d0) are constant maps Lec4.5:Thm4.1.7:(X,d) is connected iff the only continuous map of(X,d) onto(X0,d0) are constant maps