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1. On the hyperspace of bounded closed sets under a generalized Hausdorff stationary fuzzy metric

Creator:
Qiu, Dong, Lu, Chongxia, Deng, Shuai, and Wang, Liang
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Hausdorff metric, hyperspace, triangular norms, and stationary fuzzy metric
Language:
English
Description:
In this paper, we generalize the classical Hausdorff metric with t-norms and obtain its basic properties. Furthermore, for a given stationary fuzzy metric space with a t-norm without zero divisors, we propose a method for constructing a generalized Hausdorff fuzzy metric on the set of the nonempty bounded closed subsets. Finally we discuss several important properties as completeness, completion and precompactness.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On uniformly locally compact quasi-uniform hyperspaces

Creator:
Künzi, Hans-Peter A., Romaguera, Salvador , and Sánchez-Granero, M. A.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Hausdorff-Bourbaki quasi-uniformity, hyperspace, locally compact, cofinally complete, uniformly locally compact, and co-uniformly locally compact
Language:
English
Description:
We characterize those Tychonoff quasi-uniform spaces $(X,\mathcal {U})$ for which the Hausdorff-Bourbaki quasi-uniformity is uniformly locally compact on the family $\mathcal {K}_{0}(X)$ of nonempty compact subsets of $X$. We deduce, among other results, that the Hausdorff-Bourbaki quasi-uniformity of the locally finite quasi-uniformity of a Tychonoff space $X$ is uniformly locally compact on $\mathcal {K}_{0}(X)$ if and only if $X$ is paracompact and locally compact. We also introduce the notion of a co-uniformly locally compact quasi-uniform space and show that a Hausdorff topological space is $\sigma $-compact if and only if its (lower) semicontinuous quasi-uniformity is co-uniformly locally compact. A characterization of those Hausdorff quasi-uniform spaces $(X,\mathcal {U})$ for which the Hausdorff-Bourbaki quasi-uniformity is co-uniformly locally compact on $\mathcal {K}_{0}(X)$ is obtained.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. The omega limit sets of subsets in a metric space

Creator:
Ding, Changming
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
limit set of a set, attractor, quasi-attractor, and hyperspace
Language:
English
Description:
In this paper, we discuss the properties of limit sets of subsets and attractors in a compact metric space. It is shown that the $\omega $-limit set $\omega (Y)$ of $Y$ is the limit point of the sequence $\lbrace (\mathop {\mathrm Cl}Y)\cdot [i,\infty )\rbrace _{i=1}^{\infty }$ in $2^X$ and also a quasi-attractor is the limit point of attractors with respect to the Hausdorff metric. It is shown that if a component of an attractor is not an attractor, then it must be a real quasi-attractor.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public