Displaying similar documents to “A generalization of N. Aronszajn's theorem on connectedness of the fixed point set of a compact mapping”

Connectedness and Continuous Sequences in Finite Topological Spaces

Yatsuka Nakamura (2006)

Formalized Mathematics

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First, equivalence conditions for connectedness are examined for a finite topological space (originated in [9]). Secondly, definitions of subspace, and components of the subspace of a finite topological space are given. Lastly, concepts of continuous finite sequence and minimum path of finite topological space are proposed.

Embedding a topological group into a connected group

Ryo Ohashi (2007)

Colloquium Mathematicae

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It was proved in [HM] that each topological group (G,·,τ) may be embedded into a connected topological group (Ĝ,•,τ̂). In fact, two methods of introducing τ̂ were given. In this note we show relations between them.