Equality

• Suppose the property E_x(y) = (y = x) is semidecidable for each x

• Then the set { x } is semidecidable for each x

• So each singleton is open

• Then the space is discrete

Open set	=	Semidecidable property
Closed set	=	Semidecidable complement
Clopen set	=	Decidable property
Continuous function	=	Computable function
Discrete space	=	Semidecidable equality