# Topological Life

Howard A. Landman, in his paper * Eyespace Values in Go*, in *Games of No Chance*^{[1]}, defines **topological life** as follows:

- A group is said to be
*topologically alive*if (1) the units^{[2]}of the group completely surround two or more single-point eyes, and (2) each unit of the group is adjacent to at least two of those eyes.

This is clearly a sufficient but not a necessary condition for the group to be pass-alive which, as is evident from Benson's Theorem, is possible with larger eyes possibly containing enemy stones.

While Landman remarks that it is probably provable that any pass-alive group can be made topologically alive, he does not appear to use the concept of topological life in any significant way in the above paper.

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### See also

- Benson's Definition of Unconditional Life — A group is pass-alive if each of its chains has at least two eyes completely enclosed by the group
- Two Headed Dragon — A topologically alive group having two eyes that look false
- Two Eye Formation — (used in by Robert Jasiek in rules) A set of chains sharing exactly two liberties and having no others
- Fractional Eyes — A presentation of some elements of the paper
*Eyespace Values in Go*cited above

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### Notes

[1] * Games of No Chance*, Volume 29 of the MSRI Book Series

[2] Landman uses the term *unit* for a chain, i.e. a maximal strictly connected set of stones.