A Knaster--Reichbach type theorem for graph structures

2026/02/17 by Wiesław Kubiś, Andrzej Kucharski, Sławomir Turek · 1 voice
Mathematics · #math.GN #math.CT

paper · pdf

Abstract

We study the properties of a generic object ℙ in the category of finite graphs. It turns out that this object, being topologically a Cantor set, has the Knaster--Reichbach type property. Namely, every homeomorphism and isomorphism h\colon K→ L where K and L are nowhere dense closed sets in ℙ and consisting only of isolated vertices in K and L can be extended to the autohomeomorphism and autoisomorphism of the whole graph ℙ.

Citations

• On generic topological embeddings
• Evolutions of finite graphs
• Universal homomorphisms, universal structures, and the polymorphism clones of homogeneous structures
• Fraïssé sequences: category-theoretic approach to universal homogeneous structures
• Projective Fraïssé limits and the pseudo-arc

Discussions

• Wies{\l}aw Kubi\'s, Andrzej Kucharski, S{\l}awomir Turek: A Knaster--Reichbach type theorem for graph structures https://arxiv.org/abs/2602.15696 https://arxiv.org/pdf/2602.15696 https://arxiv.org/htm [bsky, 0 points, 0 comments]

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