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.

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

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.