Topology structures of the families of gray images

DOI

10.2991/icmt-13.2013.3How to use a DOI?

Keywords

Upper semi-continuous maps. Continuous maps. Vietoris topology. Regions below of maps. Hilbert cube.

Abstract

Let L be a subspace of Euclidean Space E1. USC(X,L) denote all regions below of upper semi-continuous maps from X to L and C(X,L) denote all regions below of continuous maps from X to L. For an infinite compact metric space X, USC(X,I) with Vietoris topology is homeomorphic to Hilbert cube Q and C(X,I) is its subspace, where Q=[-1, 1] . USC(X, I) could be regarded as a mathematical model of all gray images. In the present paper, the following result is proved: USC(X, [0,1)) is homeomorphic to Q{(0)}. Therefore the topological structure of C(X, [0,1)) is also clear.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Wu N.
PY  - 2013/11
DA  - 2013/11
TI  - Topology structures of the families of gray images
BT  - Proceedings of 3rd International Conference on Multimedia Technology(ICMT-13)
PB  - Atlantis Press
SP  - 19
EP  - 26
SN  - 1951-6851
UR  - https://doi.org/10.2991/icmt-13.2013.3
DO  - 10.2991/icmt-13.2013.3
ID  - N.2013/11
ER  -