| Title:
|
Further new generalized topologies via mixed constructions due to Császár (English) |
| Author:
|
Ekici, Erdal |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
140 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
1-9 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The theory of generalized topologies was introduced by Á. Császár (2002). In the literature, some authors have introduced and studied generalized topologies and some generalized topologies via generalized topological spaces due to Á. Császár. Also, the notions of mixed constructions based on two generalized topologies were introduced and investigated by Á. Császár (2009). The main aim of this paper is to introduce and study further new generalized topologies called $\mu _{12}^{C}$ via mixed constructions based on two generalized topologies $\mu _{1}$ and $\mu _{2}$ on a nonempty set $X$ and also generalized topologies called $\mu _{C}$ and $\mu _{\ast }^{C}$ for a generalized topological space $(X,\mu )$. (English) |
| Keyword:
|
mixed construction |
| Keyword:
|
generalized topology |
| Keyword:
|
generalized topological space |
| Keyword:
|
weak generalized topology |
| Keyword:
|
countable subcover |
| Keyword:
|
$\mu _{12}^{C}$-open set |
| Keyword:
|
$\mu _{C}$-open set |
| Keyword:
|
$\mu _{\ast }^{C}$-open set |
| Keyword:
|
countable set |
| MSC:
|
54A05 |
| idZBL:
|
Zbl 06433694 |
| idMR:
|
MR3324415 |
| DOI:
|
10.21136/MB.2015.144173 |
| . |
| Date available:
|
2015-03-09T17:35:54Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144173 |
| . |
| Reference:
|
[1] Császár, Á.: Generalized topology, generalized continuity.Acta Math. Hung. 96 (2002), 351-357. Zbl 1006.54003, MR 1922680, 10.1023/A:1019713018007 |
| Reference:
|
[2] Császár, Á.: Separation axioms for generalized topologies.Acta Math. Hung. 104 (2004), 63-69. Zbl 1059.54003, MR 2069962, 10.1023/B:AMHU.0000034362.97008.c6 |
| Reference:
|
[3] Császár, Á.: Generalized open sets in generalized topologies.Acta Math. Hung. 106 (2005), 53-66. Zbl 1076.54500, MR 2127051, 10.1007/s10474-005-0005-5 |
| Reference:
|
[4] Császár, Á.: Mixed constructions for generalized topologies.Acta Math. Hung. 122 (2009), 153-159. Zbl 1199.54003, MR 2487467, 10.1007/s10474-008-8002-0 |
| Reference:
|
[5] Ekici, E., Roy, B.: New generalized topologies on generalized topological spaces due to Császár.Acta Math. Hung. 132 (2011), 117-124. Zbl 1240.54006, MR 2805482, 10.1007/s10474-010-0050-6 |
| Reference:
|
[6] Min, W. K.: Some results on generalized topological spaces and generalized systems.Acta Math. Hung. 108 (2005), 171-181. Zbl 1082.54504, MR 2155250, 10.1007/s10474-005-0218-7 |
| Reference:
|
[7] Devi, V. Renuka, Sivaraj, D.: On $\delta $-sets in $\gamma $-spaces.Filomat 22 (2008), 97-106. MR 2482654 |
| Reference:
|
[8] Száz, Á.: Minimal structures, generalized topologies, and ascending systems should not be studied without generalized uniformities.Filomat 21 (2007), 87-97. Zbl 1199.54164, MR 2311042, 10.2298/FIL0701087S |
| . |
