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How exactly to interpret topological properties in terms of physical phenomena is not an easy question.
What can be objectively said is that in a non-Hausdorff space limits are not unique, which means that things like unique derivatives likewise don't exist. That means that derivative-related concepts, such as speed, can't be defined as usual. They generally become "fuzzy".
Not sure if that helps your debate along. What is the overarching reason for the question? If you're considering such abstract properties there are likely a number that anyone would dearly miss. A non-Hausdorff space for instance already is not metric, which might put them beyond what the average person consider dimensional space. Math also has like a dozen different notions of "dimensionality".
What can be objectively said is that in a non-Hausdorff space limits are not unique, which means that things like unique derivatives likewise don't exist. That means that derivative-related concepts, such as speed, can't be defined as usual. They generally become "fuzzy".
Not sure if that helps your debate along. What is the overarching reason for the question? If you're considering such abstract properties there are likely a number that anyone would dearly miss. A non-Hausdorff space for instance already is not metric, which might put them beyond what the average person consider dimensional space. Math also has like a dozen different notions of "dimensionality".
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