Continuous function

Set

context $\langle X,\mathcal{T}_X\rangle$ … topological space
context $\langle Y,\mathcal{T}_Y\rangle$ … topological space
definiendum $ f\in \mathrm{it} $
inclusion $ f:X\to Y $
for all $V\in \mathcal{T}_Y$
postulate $ f^{-1}(V)\in\mathcal{T}_X $

Discussion

Theorems

A function to $\mathbb R^n$ is continuous iff all its components are.

clarify topologies here

Parents

Context

Requirements

Subset of

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