C programs for Boundary-Border Extensions of the Kuratowski Monoid

Errata in published version (Topology and its Applications)

All topologies up to homeomorphism on n points for n = 2 to 11 can be found here.

A description of the method used to compute them is forthcoming.

For n = 2 to 6 this program confirms the spaces are topological and inequivalent.

Page numbers with an “a” refer to the arXiv preprint.

Section 2

4 (a4): Theorem 1, no further edges

6 (a6): Lemma 7, no further decompositions

7 (a7): Proposition 3, sharpness

8 (a7): Proposition 4, no further edges

Section 3

10 (a9): Footnote 19 (a20), Kleiner's OU example

11 (a10): Table 6, frequencies of the seven GE monoids

11 (a11): Proposition 6, unique minimal spaces

12 (a11): Theorem 4, KF has nine global orderings

13 (a13): Theorem 5, KFG has ten global collapses

15 (a13): Theorem 6, KFG has 12 global orderings

Section 4

15 (a15): Footnote 24, local collapses and orderings of KFGZ

17 (a18): Table 9, smallest cardinality admitting each ψ-number

17 (a19): border ψ-numbers, both possible values occur

17 (a20): ψ-numbers, only ones possible do occur

17 (a20): relative frequencies, rarest and commonest φ- and ψ-numbers

17 (a20): Figure 6, ψ-number dependencies

17 (a20): Table 10, evidence supporting Figure 6

20 (a22): Proposition 8, KFZ has 274 local orderings

(a23): Table a12, each non-blank entry occurs optionally

(a23): Table a13, local orderings of KFZ per psi-number

21 (a25): Theorem 8, KF has 496 local orderings

21 (a25): Corollary 11, K has 66 local orderings

22 (a26): Table 11 (a15), equivalences among local relations in KF

23 (a27): Figure 7 (a8), implications among local relations in KF

24 (a29): Figure 8 (a9), implications among global relations in KF

Section 5

27 (a32): Table 12 (a17), characterizations of local collapses

28 (a33): Theorem 9, sharpness

28 (a33): connected spaces, all remaining φ- and ψ-numbers occur

29 (a35): Theorem 10, all k- and k_f-number combinations occur

30 (a35-a36): Corollary 16 and Table 16 (a21,a22), intersections of φ- and ψ-numbers

31 (a37): Table 15 (a20), find all ψ-numbers in sums of minimal spaces

31 (a37): sharpness of upper bounds in Corollaries 17 and 18

32 (a34): Figure 9 (a10), meet semilattices of φ- and ψ-numbers

32 (a37): Proposition 16, φ- and ψ-numbers in various 10- and 11-spaces