# On preserving continuity in ideal topological spaces

@inproceedings{Njamcul2021OnPC, title={On preserving continuity in ideal topological spaces}, author={Anika Njamcul and Aleksandar Pavlovi'c}, year={2021} }

We present some sufficient conditions for continuity of the mapping f : 〈X, τ∗ X〉 → 〈Y, τ∗ Y 〉, where τ∗ X and τ ∗ Y are topologies induced by the local function on X and Y , resp. under the assumption that the mapping from 〈X, τX〉 to 〈Y, τY 〉 is continuous. Further, we consider open and closed functions in this matter, as we state the cases in which the open (or closed) mapping is being preserved through the ”idealisation” of both domain and codomain. Through several examples we illustrate…

## References

SHOWING 1-10 OF 23 REFERENCES

DECOMPOSITIONS OF CONTINUITY IN IDEAL TOPOLOGICAL SPACES

- Mathematics
- 2014

Abstract In this paper, we define new classes of sets called preopen sets, θI-semi-open sets, θI-β-open sets and θI-α-open sets in ideal topological spaces. Also, by using these sets, we obtain new…

Regular Weakly Continuous Functions in Ideal Topological Spaces

- Mathematics
- 2015

In this paper, we study the concepts of I rw -continuity in ideal topological spaces, and obtain several characterizations and some properties of these functions. Also, we investigate their…

A note on W-I-continuous functions

- Mathematics
- 2008

In [1], Açıkgöz et al. introduced and investigated the notions of w-I-continuous and w*-I-continuous functions in ideal topological spaces. In this paper, we investigate their relationships with…

Some characterizations of Inversely Open and Inversely Closed maps via Ideals

- 2017

We use the theory of local functions via ideals defined on a topological space to characterize inversely open and inversely closed maps between ideal spaces. AMS subject classification: 54C08, 54C10.

Topologies which generate a complete measure algebra

- Mathematics
- 1971

Topologies are constructed so that the σ-field they generate is the collection of Lebesgue-measurable sets. One such topology provides a simple proof of von Neumann's theorem on selecting…

Concerning continuity apart from a meager set

- Mathematics
- 1986

Given a a-ideal .f of subsets of a space X, mappings f: X -Y are investigatSed, such that f I XO is continuous for some closed X0 c X with X \ XA0 E .

QUASI COMPACTNESS WITH RESPECT TO AN IDEAL

- Mathematics
- 1994

~ ~t. J. JlAlI 4:S):-1 ..:.J~~I ~ ~~ X ~~I <Y I J~I ...;~ rJ+A.o '~Vy r~ (~I.) J ,~'V r~ (~~) ..f'",)l J.ilJ . ,)J.bJ.1 ,)\.l~IJ .ly~1 ~ 4:S:r:- 4U~ »:,f e;A1J c..p..;\Jaj, ~~ ~l ~ ~.1JIJ J:,~~ ~ I…

On AI -sets, CI -sets, C∗ I -sets and decompositions of continuity in ideal topological spaces. An

- Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 59,
- 2013

Notes on the continuity in ideal topological spaces

- Int. J. Pure Appl. Math. 23,
- 2005