arXiv Open Access 2024

Generically hereditarily equivalent continua and topological characterization of generic maximal chains of generalized Ważewski dendrites

Bryant Rosado Silva Benjamin Vejnar

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Abstrak

The notion of hereditarily equivalent continua is classical in continuum theory with only two known nondegenerate examples (arc, and pseudoarc). In this paper we introduce generically hereditarily equivalent continua, i.e. continua which are homeomorphic to comeager many subcontinua. We investigate this notion in the realm of Peano continua and we prove that all the generalized Ważewski dendrites are such. Consequently, we study maximal chains consisting of subcontinua of generalized Ważewski dendrites and we prove that there is always a generic orbit under the homeomorphism group action. As a part of the proof we provide a topological characterization of the generic maximal chain.

Topik & Kata Kunci

math.GN

Penulis (2)

Bryant Rosado Silva

Benjamin Vejnar

Format Sitasi

APA MLA BibTeX

Silva, B.R., Vejnar, B. (2024). Generically hereditarily equivalent continua and topological characterization of generic maximal chains of generalized Ważewski dendrites. https://arxiv.org/abs/2409.16740

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓