| Title:
|
Almost locatedness in uniform spaces (English) |
| Author:
|
Bridges, Douglas |
| Author:
|
Ishihara, Hajime |
| Author:
|
Mines, Ray |
| Author:
|
Richman, Fred |
| Author:
|
Schuster, Peter |
| Author:
|
Vîţă, Luminiţa |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
1-12 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A weak form of the constructively important notion of locatedness is lifted from the context of a metric space to that of a uniform space. Certain fundamental results about almost located and totally bounded sets are then proved. (English) |
| Keyword:
|
uniform structure |
| Keyword:
|
located |
| Keyword:
|
constructive |
| MSC:
|
03F60 |
| MSC:
|
54E15 |
| MSC:
|
54E35 |
| idZBL:
|
Zbl 1174.03027 |
| idMR:
|
MR2309944 |
| . |
| Date available:
|
2009-09-24T11:43:16Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128150 |
| . |
| Reference:
|
[1] Errett Bishop: Foundations of constructive analysis.McGraw-Hill, 1967. MR 0221878 |
| Reference:
|
[2] Errett Bishop and Douglas Bridges: Constructive Analysis.Grundlehren der math. Wissenschaften Bd. 279, Springer, Heidelberg, 1985. MR 0804042 |
| Reference:
|
[3] Douglas Bridges and Luminiţa Dediu (Vîţă): Constructive notes on uniform and locally convex spaces.Proceedings of 12th International Symposium, FCT’99, Iaşi, Romania, Springer Lecture Notes in Computer Science 1684 (1999), 195–203. MR 1850231, 10.1007/3-540-48321-7_15 |
| Reference:
|
[4] Douglas Bridges and Fred Richman: Varieties of Constructive Mathematics.London Math. Soc. Lecture Notes 97, Cambridge University Press, London, 1987. MR 0890955 |
| Reference:
|
[5] Douglas Bridges and Luminiţa Vîţă: Cauchy nets in the constructive theory of apartness spaces.Scientiae Math. Japonicae 56 (2001), 123–132. MR 1911838 |
| Reference:
|
[6] Douglas Bridges, Peter Schuster and Luminiţa Vîţă: Apartness, topology, and uniformity: a constructive view in Computability and Complexity in Analysis (Proc. Dagstuhl Seminar 01461, 11–16 November 2001, V. Brattka, P. Hertling, M. Yasugi eds.).Math. Log. Quart. 48 (2002), Suppl. 1, 16–28. MR 1948052 |
| Reference:
|
[7] Nicolas Bourbaki: General Topology (Part 1).Addison-Wesley, Reading, MA, 1966. |
| Reference:
|
[8] Robin J. Grayson: Concepts of general topology in constructive mathematics and in sheaves, II.Ann. Math. Logic 23 (1982), 55–98. MR 0674673, 10.1016/0003-4843(82)90010-9 |
| Reference:
|
[9] Peter Schuster, Douglas Bridges and Luminiţa Vîţă: Apartness as a relation between subsets.Combinatorics, Computability and Logic (Proceedings of DMTCS’01, Constanţa, Romania, 2–6 July 2001), C. S. Calude, M. J. Dinneen, S. Sburlan (eds.), DMTCS Series 17, Springer-Verlag, London, 2001, pp. 203–214. MR 1934832 |
| Reference:
|
[10] Anne S. Troelstra: Intuitionistic General Topology.PhD. Thesis, University of Amsterdam, 1966. MR 0285356 |
| Reference:
|
[11] Anne S. Troelstra and Dirk van Dalen: Constructivism in Mathematics.Studies in Mathematical Logic and the Foundations of Mathematics, 121 and 123, North-Holland, Amsterdam, 1988. |
| . |
