Decomposition of Topologies Which Characterize the Upper and Lower Semicontinuous Limits of Functions
Author
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-10-23
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We present a decomposition of two topologies which characterize the upper and lower semicontinuity of the limit function to visualize their hidden and opposite roles with respect to the upper and lower semicontinuity and consequently the continuity of the limit.
We show that (from the statistical point of view) there is an asymmetric role of the upper and lower decomposition of the pointwise convergence with respect to the upper and lower decomposition of the sticking convergence and the semicontinuity of the limit.
This role is completely hidden if we use the whole pointwise convergence.
Moreover, thanks to this mirror effect played by these decompositions, the statistical pointwise convergence of a sequence of continuous functions to a continuous function in one of the two symmetric topologies, which are the decomposition of the sticking topology, automatically ensures the convergence in the whole sticking topology.
American Psychological Association (APA)
Caserta, Agata. 2011. Decomposition of Topologies Which Characterize the Upper and Lower Semicontinuous Limits of Functions. Abstract and Applied Analysis،Vol. 2011, no. 2011, pp.1-9.
https://search.emarefa.net/detail/BIM-503806
Modern Language Association (MLA)
Caserta, Agata. Decomposition of Topologies Which Characterize the Upper and Lower Semicontinuous Limits of Functions. Abstract and Applied Analysis No. 2011 (2011), pp.1-9.
https://search.emarefa.net/detail/BIM-503806
American Medical Association (AMA)
Caserta, Agata. Decomposition of Topologies Which Characterize the Upper and Lower Semicontinuous Limits of Functions. Abstract and Applied Analysis. 2011. Vol. 2011, no. 2011, pp.1-9.
https://search.emarefa.net/detail/BIM-503806
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-503806