X is connected iff every continuous function from X to discrete space D reduce to constant function.

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space is connected iff a continuous function from X to discrete space Y reduces to constant function

Domain is Discrete m.s. then function is conti.|L24 | TYBSc Maths |Continuous Functions @ranjankhatu

Every Continuous function from connected space to a discrete space is constant|connected subset

X is connected iff there does't exist surjective cont function from X onto two point discrete space.

f implies continuous

Any const function is continuous & Any function whose domain is discrete metric space is continuous

Topology Proof The Constant Function is Continuous

Connectedness 8 (Topology): Locally Constant Functions