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Finite-dimensional maps and dendrites with dense sets of end points

Hisao Kato, Eiichi Matsuhashi (2006)

Colloquium Mathematicae

The first author has recently proved that if f: X → Y is a k-dimensional map between compacta and Y is p-dimensional (0 ≤ k, p < ∞), then for each 0 ≤ i ≤ p + k, the set of maps g in the space C ( X , I p + 2 k + 1 - i ) such that the diagonal product f × g : X → Y × I p + 2 k + 1 - i is an (i+1)-to-1 map is a dense G δ -subset of C ( X , I p + 2 k + 1 - i ) . In this paper, we prove that if f: X → Y is as above and D j (j = 1,..., k) are superdendrites, then the set of maps h in C ( X , ∏ j = 1 k D j × I p + 1 - i ) such that f × h : X → Y × ( ∏ j = 1 k D j × I p + 1 - i ) is (i+1)-to-1 is a dense G δ -subset of C ( X , ∏ j = 1 k D j × I p + 1 - i ) for each 0 ≤ i ≤ p.

Finite-to-one continuous s-covering mappings

Alexey Ostrovsky (2007)

Fundamenta Mathematicae

The following theorem is proved. Let f: X → Y be a finite-to-one map such that the restriction f | f - 1 ( S ) is an inductively perfect map for every countable compact set S ⊂ Y. Then Y is a countable union of closed subsets Y i such that every restriction f | f - 1 ( Y i ) is an inductively perfect map.

Finite-to-one maps and dimension

Jerzy Krzempek (2004)

Fundamenta Mathematicae

It is shown that for every at most k-to-one closed continuous map f from a non-empty n-dimensional metric space X, there exists a closed continuous map g from a zero-dimensional metric space onto X such that the composition f∘g is an at most (n+k)-to-one map. This implies that f is a composition of n+k-1 simple ( = at most two-to-one) closed continuous maps. Stronger conclusions are obtained for maps from Anderson-Choquet spaces and ones that satisfy W. Hurewicz's condition (α). The main tool is...

Fixed and coincidence points of hybrid mappings

H. K. Pathak, M. S. Khan (2002)

Archivum Mathematicum

The purpose of this note is to provide a substantial improvement and appreciable generalizations of recent results of Beg and Azam; Pathak, Kang and Cho; Shiau, Tan and Wong; Singh and Mishra.

Fixed point and continuation results for contractions in metric and gauge spaces

M. Frigon (2007)

Banach Center Publications

We present an overview of generalizations of Banach's fixed point theorem and continuation results for contractions, i.e., results establishing that the existence of a fixed point is preserved by suitable homotopies. We will consider single-valued and multi-valued contractions in metric and in gauge spaces.

Fixed point results for multivalued contractions on ordered gauge spaces

Gabriela Petruşel (2009)

Open Mathematics

The purpose of this article is to present fixed point results for multivalued E ≤-contractions on ordered complete gauge space. Our theorems generalize and extend some recent results given in M. Frigon [7], S. Reich [12], I.A. Rus and A. Petruşel [15] and I.A. Rus et al. [16].

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