Title:
|
Quasicontinuity and related properties of functions and multivalued maps (English) |
Author:
|
Ewert, Janina |
Language:
|
English |
Journal:
|
Mathematica Bohemica |
ISSN:
|
0862-7959 (print) |
ISSN:
|
2464-7136 (online) |
Volume:
|
120 |
Issue:
|
4 |
Year:
|
1995 |
Pages:
|
393-403 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
The main results presented in this paper concern multivalued maps. We consider the cliquishness, quasicontinuity, almost continuity and almost quasicontinuity; these properties of multivalued maps are characterized by the analogous properties of some real functions. The connections obtained are used to prove decomposition theorems for upper and lower quasicontinuity. (English) |
Keyword:
|
uniform space |
Keyword:
|
multifunctions |
Keyword:
|
decomposition theorem |
Keyword:
|
quasicontinuity |
Keyword:
|
multivalued map |
MSC:
|
26A25 |
MSC:
|
26E25 |
MSC:
|
54C08 |
MSC:
|
54C60 |
idZBL:
|
Zbl 0843.54018 |
idMR:
|
MR1415087 |
DOI:
|
10.21136/MB.1995.126086 |
. |
Date available:
|
2009-09-24T21:13:25Z |
Last updated:
|
2020-07-29 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126086 |
. |
Reference:
|
[1] D. Andrijević: Semi-preopen sets.Mat. Vestnik 38 (1986), 24-32. |
Reference:
|
[2] J. Borsík J. Doboš: On decomposition of quasicontinuity.Real Anal. Exch. 16 (1990-91), 292-305. MR 1087494, 10.2307/44153699 |
Reference:
|
[3] J. Ewert: On quasi-continuous and cliquish maps with values in uniform spaces.Bull. Polish Acad. Sci. Math. 32 (1984), 81-88. Zbl 0579.54008, MR 0766984 |
Reference:
|
[4] J. Ewert: Quasi-continuity of multivalued maps with respect to the qualitative topology.Acta Math. Hungarica 56 (1990), 39-44. Zbl 0724.54016, MR 1100774, 10.1007/BF01903703 |
Reference:
|
[5] J. Ewert: On almost quasicontinuity of functions.Tatra Mountains Math. Publ. 2 (1993), 81-91. Zbl 0835.54010, MR 1251042 |
Reference:
|
[6] L. A. Fudali: On cliquish functions on product spaces.Math. Slovaca 33 (1983), 53-58. Zbl 0512.54007, MR 0689278 |
Reference:
|
[7] H. Hashimoto: On the *-topology and its application.Fundam. Math. 91 (1976), 5-10. MR 0413058, 10.4064/fm-91-1-5-10 |
Reference:
|
[8] T. Husain: Almost continuous mappings.Prace Mat. 10 (1966), 1-7. Zbl 0138.17601, MR 0220256 |
Reference:
|
[9] S. Kempisty: Sur les fonctions quasi-continues.Fundam. Math. 19 (1932), 184-197. 10.4064/fm-19-1-184-197 |
Reference:
|
[10] N. Levine: Semi-open sets and semi-continuity in topological spaces.Amer. Math. Monthly 70 (1963), 36-41. Zbl 0113.16304, MR 0166752, 10.1080/00029890.1963.11990039 |
Reference:
|
[11] J. S. Lipiński T. Šalát: On the points of quasi-continuity and cliquishness of functions.Czechoslov. Math. J. 21 (1971), 484-489. MR 0287517 |
Reference:
|
[12] T. Neubrunn: Quasicontinuity.Real Anal. Exch. 14 (1988-89), 259-306. MR 0995972 |
Reference:
|
[13] A. Neubrunnová: On quasicontinuous and cliquish functions.Časopis Pěst. Mat. 99 (1974), 109-114. MR 0360948 |
Reference:
|
[14] A. Neubrunnová T. Šalát: On almost quasicontinuity.Math. Bohemica 117 (1992), 197-205. MR 1165897 |
Reference:
|
[15] J. C. Oxtoby: Measure and category.New York-Heidelberg-Berlin, 1971. Zbl 0217.09201 |
Reference:
|
[16] V. Popa: H-almost continuous multifunctions.Stud. Cerc. Mat. 32 (1980), 103-109. Zbl 0435.54014, MR 0581500 |
Reference:
|
[17] J. Smítal E. Stanová: On almost continuous functions.Acta Math. Univ. Comenianae 37 (1980), 147-156. MR 0645781 |
Reference:
|
[18] H. P. Thielman: Types of functions.Amer. Math. Monthly 60 (1953), 156-161. Zbl 0051.13801, MR 0052495, 10.1080/00029890.1953.11988260 |
. |