Spaces with dispersion point and size >= 3 are not homogeneous - #1828
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| If $|X|\ge 3$, $X$ can have at most one dispersion point. | ||
| See Proposition 1 in {{mathse:5146777}} or {{zb:48.0210.01}}. |
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the second reference is redundant for a simple fact like this, i would just remove it.
felixpernegger
enabled auto-merge (squash)
August 13, 2026 01:14
felixpernegger
approved these changes
Aug 13, 2026
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New T928:
has dispersion point + cardinality at least 3 => not homogeneous.This allows to derive that two more spaces are not homogeneous, including S125 (Knaster-Kuratowki fan).
https://topology.pi-base.org/spaces?q=Has+a+dispersion+point+%2B+%3FHomogeneous
https://math.stackexchange.com/a/5146777/52912