Question
Let $X$ be a set, $Y$ a topological space, and $X \xrightarrow{\varphi_\lambda} Y(\lambda$ in $\Lambda)$ a collection of mappings from $X$ to $Y$. Construct the coarsest topology on $X$ such that all these mappings are continuous.
Step 1
We need to find the coarsest topology on the set \( X \) such that a given collection of mappings \( \varphi_\lambda: X \to Y \) (for each \( \lambda \in \Lambda \)) are continuous, where \( Y \) is a topological space. Show more…
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