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Strongly Hit and Far Miss Hypertopology and Hit and Strongly Far Miss Hypertopology

Peters, J. F.; Guadagni, C.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/03/2015 Português
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This article introduces the {\it strongly hit and far-miss as well as hit and strongly far miss hypertopologies on $\textrm{CL}(X)$ associated with} ${\mathscr{B}}$, a nonempty family of subsets on the topological space $X$. They result from the strong farness and strong nearness proximities. The main results in this paper stem from the Hausdorffness of $(\textrm{CL}(X), \tau_{\doublevee, \mathscr{B}})$ and $(\textrm{RCL}(X), \tau^\doublewedge_\mathscr{B} ) $, where $\textrm{RCL}(X)$ is the space of regular closed subsets of $X$. To obtain the results, special local families are introduced.; Comment: 8 pages, 4 figures. arXiv admin note: text overlap with arXiv:1502.05913

Strongly far proximity and hyperspace topology

Peters, J. F.; Guadagni, C.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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This article introduces strongly far proximity, which is associated with Lodato proximity $\delta$. A main result in this paper is the introduction of a hit-and-miss topology on $\mbox{CL}(X)$, the hyperspace of nonempty closed subsets of $X$, based on the strongly far proximity.; Comment: 6 pages, 1 figure

Strongly Proximal Continuity \& Strong Connectedness

Peters, J. F.; Guadagni, C.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 10/04/2015 Português
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This article introduces strongly proximal continuous (s.p.c.) functions, strong proximal equivalence (s.p.e.) and strong connectedness. A main result is that if topological spaces $X,Y$ are endowed with compatible strong proximities and $f:X\longrightarrow Y$ is a bijective s.p.e., then its extension on the hyperspaces $\CL(X)$ and $\CL(Y)$, endowed with the related strongly hit and miss hypertopologies, is a homeomorphism. For a topological space endowed with a strongly near proximity, strongly proximal connectedness implies connectedness but not conversely. Conditions required for strongly proximal connectedness are given. Applications of s.p.c. and strongly proximal connectedness are given in terms of strongly proximal descriptive proximity.; Comment: 11 pages, 10 figures

Strongly near proximity \& hyperspace topology

Peters, J. F.; Guadagni, C.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
18.503782%
This article introduces strongly near proximity, which represents a new kind of proximity called \emph{almost proximity}. A main result in this paper is the introduction of a hit-and-miss topology on ${CL}(X)$, the hyperspace of nonempty closed subsets of $X$, based on the strongly near proximity.; Comment: 7 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1502.02771