Abstract In this paper, we define and investigate weak local functions and *-weak structures parallel to local functions and *-topology, respectively. We construct a topology from a weak structure and an ideal under the assumption that the weak structure is closed under finite intersection. In the last section we define and investigate the notion of w-extermally disconnected.

# Annals of the Alexandru Ioan Cuza University - Mathematics

### The Journal of "Alexandru Ioan Cuza" University from Iasi

Editor-in-Chief: Oniciuc, Cezar

2 Issues per year

CiteScore 2016: 0.34

SCImago Journal Rank (SJR) 2016: 0.231

Source Normalized Impact per Paper (SNIP) 2016: 0.488

Mathematical Citation Quotient (MCQ) 2015: 0.10

# A Topology Induced by Weak Structures Due to Császár and Ideals

#### Open Access

Keywords : weak structure; ideal space; weak local function

## References

1. Andrijević, D. - Some properties of the topology of -sets, Mat. Vesnik, 38 (1984), 1-10.Google Scholar

2. Császár, á. - Generalized topology, generalized continuity, Acta Math. Hungar., 96(2002), 351-357.Google Scholar

3. Császár, á. - Weak structures, Acta Math. Hungar., 131 (2011), 193-195.Web of ScienceGoogle Scholar

4. Janković, D.; Hamlett, T.R. - New topologies from old via ideals, Amer. Math.Monthly, 97 (1990), 295-310.Google Scholar

5. Kuratowski, K. - Topology I, Academic Press, New York, 1966.Google Scholar

6. Levine, N. - Semi-open sets and semi-continuity in topological spaces, Amer. Math.Monthly, 70 (1963), 36-41.Google Scholar

7. Maki, H.; Umehara, J.; Noiri, T. - Every topological space is pre-T1=2, Mem. Fac.Sci. Kochi Univ. Ser. A Math., 17 (1996), 33-42.Google Scholar

8. NjÅstad, O. - On some classes of nearly open sets, Pacific J. Math., 15 (1965),961-970.Google Scholar

9. Noiri, T. - On α-continuous functions, Casopis Pest. Mat., 109 (1984), 118-126.Google Scholar

10. Ozbakir, O.B.; Yildirim, E.D. - On some closed sets in ideal minimal spaces, ActaMath. Hungar., 125 (2009), 227-235.Google Scholar

11. Vaidyanathaswamy, R. - Set Topology, 2nd ed. Chelsea Publishing Co., New York,1960.Google Scholar

## About the article

**Received**: 2012-04-02

**Revised**: 2012-10-10

**Accepted**: 2012-10-16

**Published Online**: 2014-07-16

**Citation Information: **Annals of the Alexandru Ioan Cuza University - Mathematics, ISSN (Online) 1221-8421, DOI: https://doi.org/10.2478/aicu-2014-0022.

© Alexandru Ioan Cuza University in Iaşi . This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

## Comments (0)