preprint · arXiv (Cornell University) · 2015
Strongly Proximal Continuity \& Strong Connectedness
Cited by 3Open access
Abstract
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.
Cite this paper
Peters, J. F., & Guadagni, C. (2015). Strongly Proximal Continuity \& Strong Connectedness. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1504.02740
Peters, James F., and C. Guadagni. “Strongly Proximal Continuity \& Strong Connectedness.” arXiv (Cornell University), 2015, https://doi.org/10.48550/arxiv.1504.02740.
Peters, James F., and C. Guadagni. 2015. “Strongly Proximal Continuity \& Strong Connectedness.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.1504.02740.
Peters, J.F. and Guadagni, C. (2015) ‘Strongly Proximal Continuity \& Strong Connectedness’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.1504.02740.
@misc{peters2015strongly,
title = {{Strongly Proximal Continuity \& Strong Connectedness}},
author = {Peters, James F. and Guadagni, C.},
journal = {arXiv (Cornell University)},
year = {2015},
doi = {10.48550/arxiv.1504.02740}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.