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F σ -absorbing sequences in hyperspaces of subcontinua

Helma Gladdines (1993)

Commentationes Mathematicae Universitatis Carolinae

Let 𝒟 denote a true dimension function, i.e., a dimension function such that 𝒟 ( ℝ n ) = n for all n . For a space X , we denote the hyperspace consisting of all compact connected, non-empty subsets by C ( X ) . If X is a countable infinite product of non-degenerate Peano continua, then the sequence ( 𝒟 ≥ n ( C ( X ) ) ) n = 2 ∞ is F σ -absorbing in C ( X ) . As a consequence, there is a homeomorphism h : C ( X ) → Q ∞ such that for all n , h [ { A ∈ C ( X ) : 𝒟 ( A ) ≥ n + 1 } ] = B n × Q × Q × ⋯ , where B denotes the pseudo boundary of the Hilbert cube Q . It follows that if X is a countable infinite product of non-degenerate...

Finite topological spaces.

Juan A. Navarro González (1990)

Extracta Mathematicae

We show that the study of topological T0-spaces with a finite number of points agrees essentially with the study of polyhedra, by means of the geometric realization of finite spaces. In this paper all topological spaces are assumed to be T0.

Fixed point theory and the K-theoretic trace

Ross Geoghegan, Andrew Nicas (1999)

Banach Center Publications

The relationship between fixed point theory and K-theory is explained, both classical Nielsen theory (versus K 0 ) and 1-parameter fixed point theory (versus K 1 ). In particular, various zeta functions associated with suspension flows are shown to come in a natural way as “traces” of “torsions” of Whitehead and Reidemeister type.

Fixed point theory for homogeneous spaces, II

Peter Wong (2005)

Fundamenta Mathematicae

Let G be a compact connected Lie group, K a closed subgroup and M = G/K the homogeneous space of right cosets. Suppose that M is orientable. We show that for any selfmap f: M → M, L(f) = 0 ⇒ N(f) = 0 and L(f) ≠ 0 ⇒ N(f) = R(f) where L(f), N(f), and R(f) denote the Lefschetz, Nielsen, and Reidemeister numbers of f, respectively. In particular, this implies that the Lefschetz number is a complete invariant, i.e., L(f) = 0 iff f is deformable to be fixed point free. This was previously known under...

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