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Question regarding compactified and higher spatial dimensions

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Aight guys if you have a n-dimensional structure which also contains some compactified spatial dimensions, and you have an infinite (n+1)dimensional structure encompassing it, would it also extend infinitely in the compactified spatial dimensions?

Even if it doesn't then would it still be stronger than a n-dimensional structure that doesn't contain any compactified spatial dimensions? Since it still extends in a higher dimension since even if some dimensions are compactified they're qaulitatively still there hence a higher dimension should logically extend in a completely new axis🤔
 
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