Disjoint mappings and the span of spaces

Lelek, A.

doi:10.4064/fm-55-3-199-214

Cited by 48 publications

(26 citation statements)

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“…The span σ(/) of a 162 A. LELEK mapping / was originally defined by Ingram [3], while the present author earlier introduced the span σ(X) and, subsequently, the other types of these quantities for metric spaces (see [6] and [7]). It is known that, for some particular spaces, neither two of these four types of spans need to be equal (see [7] and [8]).…”

Section: (C a ) K)mentioning

confidence: 99%

Continua of constant distances in span theory

Lelek¹

1986

Pacific J. Math.

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Section: (C a ) K)mentioning

confidence: 99%

Continua of constant distances in span theory

Lelek¹

1986

Pacific J. Math.

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“…We utilize the following theorem from [3] in the proof of Corollary 2. Theorem L: If Y is a closed subset of the Hilbert cube I ω and ρ : Y → S is an essential mapping of Y onto the circumference S, then…”

Section: Preliminariesmentioning

confidence: 99%

The spans of five star-like simple closed curves

Thelma¹

2007

Glas. Mat. Ser. III

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Abstract. Let X be a continuum, that is a compact, connected, nonempty metric space. The span of X is the least upper bound of the set of real numbers r which satisfy the following conditions: there exists a continuum, C, contained in X × X such that d(x, y) is larger than or equal to r for all (x, y) in C and p 1 (C) = p 2 (C), where p 1 , p 2 are the usual projection maps. The following question has been asked. If X and Y are two simple closed curves in the plane and Y is contained in the bounded component of the plane minus X, then is the span of X larger than the span of Y ? We define a set of simple closed curves, which we refer to as being five star-like. We answer this question in the affirmative when X is one of these simple closed curves. We calculate the spans of the simple closed curves in this collection and consider the spans of various geometric objects related to these simple closed curves.

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“…According to (2), the centers of these balls are of distance greater than or equal to w(T') from each other. Thus these three balls are pairwise disjoint closed subsets of T, and there exists a number r\ > 0 such that if x, y G T and the points x, y belong to two different balls 50,5i,i?2, then d(x,y) > n. Let 6¿ denote the endpoint of the arc L = L¿ different from v, so that a% G L and bt may coincide with o¿, but not necessarily.…”

Section: Theorem Ift' Ct Are Simple Triods Then A*(t) > W(t')/2mentioning

confidence: 99%