Definition talk:Linear Combination of Subsets of Vector Space/Dilation

Do we really need a separate definition for this as a specific subdef of Definition:Linear Combination of Subsets of Vector Space where in fact it is an instance of a Definition:Dilation Mapping? If we silo definitions like this out into all the different contexts into which they can be applied, we will be in danger of losing the commonality of all the definitions.

So: does it make sense to scrap this definition page as it is exactly the same concept as Definition:Dilation Mapping to which we can justifiably refer to directly? --prime mover (talk) 08:27, 15 June 2023 (UTC)

"Dilation mapping" refers to the function taking $\tuple {\lambda, x}$ to $\lambda x$. This is talking about a set which is the image of that mapping under $\set \lambda \times A$. I put up this page because I needed to argue that if $U$ is open, so is $\lambda U$, and so on. Caliburn (talk) 08:29, 15 June 2023 (UTC)

Argh, it's all so fragmented! All this is, really, is a generalisation of Definition:Scalar Product to where the right hand operand is a set rather than an element. Do we need to hide this under Definition:Linear Combination of Subsets of Vector Space? Can we at least be consistent in using the redirect Definition:Dilation of Subset of Vector Space instead? I know it's something you've been pushing back against, but this is a specific case in point where we really do need to use the redirect. --prime mover (talk) 08:45, 15 June 2023 (UTC)