Dense Continuity and Selections of Set-Valued Mappings

Kenderov, Petar, Moors, Warren, and Revalski, Julian. "Dense Continuity and Selections of Set-Valued Mappings." Serdica Mathematical Journal 24.1 (1998): 49-72. <http://eudml.org/doc/11578>.

@article{Kenderov1998,
abstract = {∗ The first and third author were partially supported by National Fund for Scientific Research at the Bulgarian Ministry of Science and Education under grant MM-701/97.A theorem proved by Fort in 1951 says that an upper or lower semi-continuous set-valued mapping from a Baire space A into non-empty compact subsets of a metric space is both lower and upper semi-continuous at the points of a dense Gδ -subset of A. In this paper we show that the conclusion of Fort’s theorem holds under the weaker hypothesis of either upper or lower quasi-continuity. The existence of densely defined continuous selections for lower quasi-continuous mappings is also proved.},
author = {Kenderov, Petar, Moors, Warren, Revalski, Julian},
journal = {Serdica Mathematical Journal},
keywords = {Set-Valued Mappings; Selections, Semi-Continuity; Quasi-Continuity; Generic; Baire Category; set-valued mappings; selections; semi-continuity; Baire category; quasi-continuity},
language = {eng},
number = {1},
pages = {49-72},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Dense Continuity and Selections of Set-Valued Mappings},
url = {http://eudml.org/doc/11578},
volume = {24},
year = {1998},
}

TY - JOUR
AU - Kenderov, Petar
AU - Moors, Warren
AU - Revalski, Julian
TI - Dense Continuity and Selections of Set-Valued Mappings
JO - Serdica Mathematical Journal
PY - 1998
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 24
IS - 1
SP - 49
EP - 72
AB - ∗ The first and third author were partially supported by National Fund for Scientific Research at the Bulgarian Ministry of Science and Education under grant MM-701/97.A theorem proved by Fort in 1951 says that an upper or lower semi-continuous set-valued mapping from a Baire space A into non-empty compact subsets of a metric space is both lower and upper semi-continuous at the points of a dense Gδ -subset of A. In this paper we show that the conclusion of Fort’s theorem holds under the weaker hypothesis of either upper or lower quasi-continuity. The existence of densely defined continuous selections for lower quasi-continuous mappings is also proved.
LA - eng
KW - Set-Valued Mappings; Selections, Semi-Continuity; Quasi-Continuity; Generic; Baire Category; set-valued mappings; selections; semi-continuity; Baire category; quasi-continuity
UR - http://eudml.org/doc/11578
ER -