Details
| Original language | English |
|---|---|
| Pages (from-to) | 13-28 |
| Number of pages | 16 |
| Journal | Mathematische Nachrichten |
| Volume | 147 |
| Issue number | 1 |
| Publication status | Published - 19 Nov 2010 |
Abstract
The classical order‐theoretical characterizations of compact and connected chains, respectively, are extended to wider classes of lattices, using the fact that compactness and (path‐) connectedness of maximal chains are closely related to the corresponding properties of the whole lattice (as was already pointed out in an earlier paper due to the second author). Here we replace maximal chains by “links” and study several new types of connectedness in ordered convergence spaces, such as path‐connectedness, link‐connectedness and 1‐connectedness. As a useful framework for these studies, we introduce the concept of “connectivity systems”.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Mathematische Nachrichten, Vol. 147, No. 1, 19.11.2010, p. 13-28.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Connectivity in Lattice‐Ordered Spaces
AU - Erné, M.
AU - Vainio, R.
PY - 2010/11/19
Y1 - 2010/11/19
N2 - The classical order‐theoretical characterizations of compact and connected chains, respectively, are extended to wider classes of lattices, using the fact that compactness and (path‐) connectedness of maximal chains are closely related to the corresponding properties of the whole lattice (as was already pointed out in an earlier paper due to the second author). Here we replace maximal chains by “links” and study several new types of connectedness in ordered convergence spaces, such as path‐connectedness, link‐connectedness and 1‐connectedness. As a useful framework for these studies, we introduce the concept of “connectivity systems”.
AB - The classical order‐theoretical characterizations of compact and connected chains, respectively, are extended to wider classes of lattices, using the fact that compactness and (path‐) connectedness of maximal chains are closely related to the corresponding properties of the whole lattice (as was already pointed out in an earlier paper due to the second author). Here we replace maximal chains by “links” and study several new types of connectedness in ordered convergence spaces, such as path‐connectedness, link‐connectedness and 1‐connectedness. As a useful framework for these studies, we introduce the concept of “connectivity systems”.
UR - http://www.scopus.com/inward/record.url?scp=84985405456&partnerID=8YFLogxK
U2 - 10.1002/mana.19901470103
DO - 10.1002/mana.19901470103
M3 - Article
AN - SCOPUS:84985405456
VL - 147
SP - 13
EP - 28
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
IS - 1
ER -