| Title:
|
Continuity of order-preserving functions (English) |
| Author:
|
Lavrič, Boris |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
4 |
| Year:
|
1997 |
| Pages:
|
645-655 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let the spaces $\bold R^m$ and $\bold R^n$ be ordered by cones $P$ and $Q$ respectively, let $A$ be a nonempty subset of $\bold R^m$, and let $f:A\longrightarrow \bold R^n$ be an order-preserving function. Suppose that $P$ is generating in $\bold R^m$, and that $Q$ contains no affine line. Then $f$ is locally bounded on the interior of $A$, and continuous almost everywhere with respect to the Lebesgue measure on $\bold R^m$. If in addition $P$ is a closed halfspace and if $A$ is connected, then $f$ is continuous if and only if the range $f(A)$ is connected. (English) |
| Keyword:
|
order-preserving function |
| Keyword:
|
ordered vector space |
| Keyword:
|
cone |
| Keyword:
|
solid set |
| Keyword:
|
continuity |
| MSC:
|
26B05 |
| MSC:
|
26B35 |
| MSC:
|
47H07 |
| idZBL:
|
Zbl 0942.26022 |
| idMR:
|
MR1601672 |
| . |
| Date available:
|
2009-01-08T18:37:04Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118963 |
| . |
| Reference:
|
[1] Debreu G.: Continuity properties of Paretian utility.Internat. Econom. Rev. 5 (1964), 285-293. |
| Reference:
|
[2] Fishburn P.C.: Utility Theory for Decision Making.J. Wiley and Sons, New York, London, Sidney, Toronto, 1970. MR 0264810 |
| Reference:
|
[3] Jameson G.: Ordered linear spaces.Lecture Notes in Math., Vol. 141, Springer-Verlag, Berlin, Heidelberg, New York, 1970. MR 0438077 |
| Reference:
|
[4] Lavrič B.: Continuity of monotone functions.Arch. Math. 29 (1993), 1-4. MR 1242622 |
| Reference:
|
[5] Rockafellar R.T.: Convex Analysis.Princeton Univ. Press, Princeton, N.J., 1972. MR 1451876 |
| Reference:
|
[6] Stoer J., Witzgall C.: Convexity and Optimization in Finite Dimensions I.Springer-Verlag, Berlin, 1970. MR 0286498 |
| . |
