Displaying similar documents to “A note on characterizations of compactness.”

R -continuous functions.

Konstadilaki-Savvopoulou, Ch., Janković, D. (1992)

International Journal of Mathematics and Mathematical Sciences

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The fundamental group of a locally finite graph with ends-a hyperfinite approach

Isaac Goldbring, Alessandro Sisto (2016)

Fundamenta Mathematicae

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The end compactification |Γ| of a locally finite graph Γis the union of the graph and its ends, endowed with a suitable topology. We show that π₁(|Γ|) embeds into a nonstandard free group with hyperfinitely many generators, i.e. an ultraproduct of finitely generated free groups, and that the embedding we construct factors through an embedding into an inverse limit of free groups. We also show how to recover the standard description of π₁(|Γ|) given by Diestel and Sprüssel (2011). Finally,...

Colouring of cycles in the de Bruijn graphs

Ewa Łazuka, Jerzy Żurawiecki (2000)

Discussiones Mathematicae Graph Theory

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We show that the problem of finding the family of all so called the locally reducible factors in the binary de Bruijn graph of order k is equivalent to the problem of finding all colourings of edges in the binary de Bruijn graph of order k-1, where each vertex belongs to exactly two cycles of different colours. In this paper we define and study such colouring for the greater class of the de Bruijn graphs in order to define a class of so called regular factors, which is not so difficult...