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Chebyshev Distance

100%
Coghetto R.
Formalized Mathematics
|
2016
|
tom 24
|
nr 2
121-141
EN
In [21], Marco Riccardi formalized that ℝN-basis n is a basis (in the algebraic sense defined in [26]) of [...] ℰTn ${\cal E}_T^n $ and in [20] he has formalized that [...] ℰTn ${\cal E}_T^n $ is second-countable, we build (in the topological sense defined in [23]) a denumerable base of [...] ℰTn ${\cal E}_T^n $ . Then we introduce the n-dimensional intervals (interval in n-dimensional Euclidean space, pavé (borné) de ℝn [16], semi-intervalle (borné) de ℝn [22]). We conclude with the definition of Chebyshev distance [11].
2
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Locallyn-Connected Compacta and UV n -Maps

64%
Valov V.
Analysis and Geometry in Metric Spaces
|
2015
|
tom 3
|
nr 1
EN
We provide a machinery for transferring some properties of metrizable ANR-spaces to metrizable LCn-spaces. As a result, we show that for completely metrizable spaces the properties ALCn, LCn and WLCn coincide to each other. We also provide the following spectral characterizations of ALCn and celllike compacta: A compactum X is ALCn if and only if X is the limit space of a σ-complete inverse system S = {Xα , pβ α , α < β < τ} consisting of compact metrizable LCn-spaces Xα such that all bonding projections pβα, as a well all limit projections pα, are UVn-maps. A compactum X is a cell-like (resp., UVn) space if and only if X is the limit space of a σ-complete inverse system consisting of cell-like (resp., UVn) metrizable compacta.
3
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Convergence and stability of generalizedφ-weak contraction mapping inCAT(0) spaces

64%
Kim K. S.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1063-1074
EN
The aim of this paper is to prove some fixed point results for generalized φ-weak contraction mapping and study a new concept of stability which is called comparably almost T-stable by using iterative schemes in CAT(0) spaces.
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