The set of continuous functions between topological spaces

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Let [ilmath](X,\mathcal{ J })[/ilmath] and [ilmath](Y,\mathcal{ K })[/ilmath] be topological spaces. Then [ilmath]C(X,Y)[/ilmath] denotes the set of all continuous functions from [ilmath]X[/ilmath] to [ilmath]Y[/ilmath], with respect to the topologies: [ilmath]\mathcal{J} [/ilmath] and [ilmath]\mathcal{K} [/ilmath].

That is to say:

  • [ilmath]\big(f\in C(X,Y)\big)\iff\big(f:X\rightarrow Y\text{ is a continuous function}\big)[/ilmath]

See also


  1. Both [ilmath]V[/ilmath] and [ilmath]W[/ilmath] must be over the same field


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