On Topological Spaces Defined by $${\mathcal {I}}$$-Convergence

Zhou, Xiaowen; Liu, Li; Lin, Shou

doi:10.1007/s41980-019-00284-6

Cited by 12 publications

(11 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Pal [12] for an ideal I on ω. An equivalent definition was suggested by Zhou et al [13] and further obtain that class of I-sequential spaces includes sequential spaces [5].…”

Section: K -Sequential Spacementioning

confidence: 99%

Further aspects of I K-convergence in topological spaces

Sharmah

Hazarika

2021

Appl. Gen. Topol.

View full text Add to dashboard Cite

In this paper, we obtain some results on the relationships between different ideal convergence modes namely, I K, I K∗ , I, K, I ∪ K and (I ∪K) ∗ . We introduce a topological space namely I K-sequential space and show that the class of I K-sequential spaces contain the sequential spaces. Further I K-notions of cluster points and limit points of a function are also introduced here. For a given sequence in a topological space X, we characterize the set of I K-cluster points of the sequence as closed subsets of X.

show abstract

“…Pal [12] for an ideal I on ω. An equivalent definition was suggested by Zhou et al [13] and further obtain that class of I-sequential spaces includes sequential spaces [5].…”

Section: K -Sequential Spacementioning

confidence: 99%

Further aspects of I K-convergence in topological spaces

Sharmah

Hazarika

2021

Appl. Gen. Topol.

View full text Add to dashboard Cite

show abstract

“…The J -sequential coreflection of a space X is the set X endowed with the topology consisting of J -open subsets of X, which is denoted by J -sX. The spaces X and J -sX have the same J -convergent sequences; J -sX is an J -sequential space; a space X is an J -sequential space if and only if J -sX = X [20].…”

Section: Definition 27 ([20]mentioning

confidence: 99%

“…In [20], it was discussed that quotient mappings, sequentially quotient mappings and I-quotient mappings are mutually independent; and the following two theorems are useful and can be seen in it.…”

Section: I-quotient Mappingsmentioning

confidence: 99%

“…(1) A space X is called I-Fréchet-Urysohn (or shortly, I-FU) space, if for each A ⊂ X and each x ∈ A, there exists a sequence in A I-converging to the point x in X [20]. (2) A space X is called a meta-Lindelöf space if each open cover of X has a point-countable open refinement [13].…”

Section: Zhoumentioning

confidence: 99%

“…[20]). If J is a maximal ideal of N, then A ⊆ X is J -open if and only if for each J -converging sequence{x n } n∈N with x n J − → x ∈ A, then {x n } n∈N is J -eventually in A.By Definition 2.2, the union of a family of I-open sets in a topological space is I-open.…”

mentioning

confidence: 99%

See 2 more Smart Citations

On I-quotient mappings and I-cs'-networks under a maximal ideal

Zhou

2020

Appl. Gen. Topol.

Self Cite

View full text Add to dashboard Cite

<p>Let I be an ideal on N and f : X → Y be a mapping. f is said to be an I-quotient mapping provided f−1(U) is I-open in X, then U is I-open in Y . P is called an I-cs′-network of X if whenever {xn}n∈N is a sequence I-converging to a point x ∈ U with U open in X, then there is P ∈ P and some n0 ∈ N such that {x, xn0} ⊆ P ⊆ U. In this paper, we introduce the concepts of I-quotient mappings and I-cs′-networks, and study some characterizations of I-quotient mappings and I-cs′- networks, especially J -quotient mappings and J -cs′-networks under a maximal ideal J of N. With those concepts, we obtain that if X is an J -FU space with a point-countable J -cs′-network, then X is a meta-Lindelöf space.</p>

show abstract

On $$\mathcal {I}$$-neighborhood Spaces and $$\mathcal {I}$$-quotient Spaces

Lin

2020

Bull. Malays. Math. Sci. Soc.

View full text Add to dashboard Cite

On Topological Spaces Defined by $${\mathcal {I}}$$-Convergence

Cited by 12 publications

References 28 publications

Further aspects of I K-convergence in topological spaces

Further aspects of I K-convergence in topological spaces

On I-quotient mappings and I-cs'-networks under a maximal ideal

On $$\mathcal {I}$$-neighborhood Spaces and $$\mathcal {I}$$-quotient Spaces

Contact Info

Product

Resources

About