On confluently graph-like compacta

• Autorzy: Lex G. Oversteegen , Janusz R. Prajs
• Języki publikacji: EN

Abstrakty

EN

For any class 𝒦 of compacta and any compactum X we say that: (a) X is confluently 𝒦-representable if X is homeomorphic to the inverse limit of an inverse sequence of members of 𝒦 with confluent bonding mappings, and (b) X is confluently 𝒦-like provided that X admits, for every ε >0, a confluent ε-mapping onto a member of 𝒦. The symbol 𝕃ℂ stands for the class of all locally connected compacta. It is proved in this paper that for each compactum X and each family 𝒦 of graphs, X is confluently 𝒦-representable if and only if X is confluently 𝒦-like. We also show that for any compactum the properties of: (1) being confluently graph-representable, and (2) being 1-dimensional and confluently 𝕃ℂ-like, are equivalent. Consequently, all locally connected curves are confluently graph-representable. We also conclude that all confluently arc-like continua are homeomorphic to inverse limits of arcs with open bonding mappings, and all confluently tree-like continua are absolute retracts for hereditarily unicoherent continua.

Kategorie tematyczne

• 54C10: Special maps on topological spaces (open, closed, perfect, etc.)
• 54F15: Continua and generalizations
• 54C15: Retraction
• 54C20: Extension of maps
• 54D05: Connected and locally connected spaces (general aspects)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 178
• Numer: 2
• Strony: 109-127

Daty

wydano

2003

Twórcy

autor

Lex G. Oversteegen

• Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, U.S.A.

autor

Janusz R. Prajs

• Institute of Mathematics, University of Opole, Oleska 48, 45-052 Opole, Poland
• Department of Mathematics, Idaho State University, Pocatello, ID 83209, U.S.A.

Identyfikatory

DOI

10.4064/fm178-2-2