scholarly journals Bounded sobriety and k-bounded sobriety of Q-cotopological spaces

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 2095-2106 ◽  
Author(s):  
Yujing Zhang ◽  
Kaiyun Wang
Keyword(s):  
Topological Space ◽  
Fuzzy Topology ◽  
Reflective Subcategory

In this paper, we extend bounded sobriety and k-bounded sobriety to the setting of Q-cotopological spaces, whereQis a commutative and integral quantale. The main results are: (1) The category BSobQ-CTop of all bounded sober Q-cotopological spaces is a full reflective subcategory of the category SQ-CTop of all stratified Q-cotopological spaces; (2) We present the relationships among Hausdorff, T1, sobriety, bounded sobriety and k-bounded sobriety in the setting ofQ-cotopological spaces; (3) For a linearly ordered quantale Q, a topological space X is bounded (resp., k-bounded) sober if and only if the corresponding Q-cotopological space ?Q(X) is bounded (resp., k-bounded) sober, where ?Q : Top ? SQ-CTop is the well-known Lowen functor in fuzzy topology.

scholarly journals A Tychonoff theorem in intuitionistic fuzzy topological spaces

2004 ◽  
Vol 2004 (70) ◽  
pp. 3829-3837
Author(s):  
Doğan Çoker ◽  
A. Haydar Eş ◽  
Necla Turanli
Keyword(s):  
Topological Space ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Tychonoff Theorem

The purpose of this paper is to prove a Tychonoff theorem in the so-called “intuitionistic fuzzy topological spaces.” After giving the fundamental definitions, such as the definitions of intuitionistic fuzzy set, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy compactness, and fuzzy dicompactness, we obtain several preservation properties and some characterizations concerning fuzzy compactness. Lastly we give a Tychonoff-like theorem.

scholarly journals Fuzzy Counterparts of Fischer Diagonal Condition in ⊤-Convergence Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 685
Author(s):  
Qiu Jin ◽  
Lingqiang Li ◽  
Jing Jiang
Keyword(s):  
Topological Space ◽  
Fuzzy Topology ◽  
Convergence Space ◽  
Convergence Spaces ◽  
Different Types ◽  
Diagonal Condition ◽  
Operator Convergence

Fischer diagonal condition plays an important role in convergence space since it precisely ensures a convergence space to be a topological space. Generally, Fischer diagonal condition can be represented equivalently both by Kowalsky compression operator and Gähler compression operator. ⊤-convergence spaces are fundamental fuzzy extensions of convergence spaces. Quite recently, by extending Gähler compression operator to fuzzy case, Fang and Yue proposed a fuzzy counterpart of Fischer diagonal condition, and proved that ⊤-convergence space with their Fischer diagonal condition just characterizes strong L-topology—a type of fuzzy topology. In this paper, by extending the Kowalsky compression operator, we present a fuzzy counterpart of Fischer diagonal condition, and verify that a ⊤-convergence space with our Fischer diagonal condition precisely characterizes topological generated L-topology—a type of fuzzy topology. Hence, although the crisp Fischer diagonal conditions based on the Kowalsky compression operator and the on Gähler compression operator are equivalent, their fuzzy counterparts are not equivalent since they describe different types of fuzzy topologies. This indicates that the fuzzy topology (convergence) is more complex and varied than the crisp topology (convergence).

ON THE SPECTRALIFICATION OF A HEMISPECTRAL SPACE

2011 ◽  
Vol 10 (04) ◽  
pp. 687-699
Author(s):  
OTHMAN ECHI ◽  
MOHAMED OUELD ABDALLAHI
Keyword(s):  
Topological Space ◽  
Open Subset ◽  
Full Subcategory ◽  
Topological Spaces ◽  
Open Problems ◽  
Complete Answer ◽  
Reflective Subcategory ◽  
Continuous Map ◽  
Open Set ◽  
Spectral Spaces

An open subset U of a topological space X is called intersection compact open, or ICO, if for every compact open set Q of X, U ∩ Q is compact. A continuous map f of topological spaces will be called spectral if f-1 carries ICO sets to ICO sets. Call a topological space Xhemispectral, if the intersection of two ICO sets of X is an ICO. Let HSPEC be the category whose objects are hemispectral spaces and arrows spectral maps. Let SPEC be the full subcategory of HSPEC whose objects are spectral spaces. The main result of this paper proves that SPEC is a reflective subcategory of HSPEC. This gives a complete answer to Problem BST1 of "O. Echi, H. Marzougui and E. Salhi, Problems from the Bizerte–Sfax–Tunis seminar, in Open Problems in Topology II, ed. E. Pearl (Elsevier, 2007), pp. 669–674."

scholarly journals More on Fuzzy Topological Spaces on Fuzzy Space

2021 ◽  
Vol 8 ◽  
pp. 21-26
Author(s):  
Abd Ulazeez Alkouri ◽  
Mohammad Hazaimeh ◽  
Ibrahim Jawarneh
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Separation Axioms ◽  
Fuzzy Space ◽  
Different Types ◽  
Fuzzy Topological Space ◽  
Isolated Points ◽  
Fuzzy Topological Spaces ◽  
Fuzzy Subsets

The fuzzy topological space was introduced by Dip in 1999 depending on the notion of fuzzy spaces. Dip’s approach helps to rectify the deviation in some definitions of fuzzy subsets in fuzzy topological spaces. In this paper, further definitions, and theorems on fuzzy topological space fill the lack in Dip’s article. Different types of fuzzy topological space on fuzzy space are presented such as co-finite, co-countable, right and left ray, and usual fuzzy topology. Furthermore, boundary, exterior, and isolated points of fuzzy sets are investigated and illustrated based on fuzzy spaces. Finally, separation axioms are studied on fuzzy spaces

scholarly journals Connectedness concept in intuitionistic fuzzy topological spaces

2021 ◽  
Vol 27 (1) ◽  
pp. 72-82
Author(s):  
Md. Aman Mahbub ◽  
◽  
Md. Sahadat Hossain ◽  
M. Altab Hossain ◽  
◽  
...  
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

The purpose of this paper is to establish the connectedness in intuitionistic fuzzy topological space. In this paper we give six notions of separatedness, connectedness and total connectedness and one notion of T1-space in intuitionistic fuzzy topological space. Also, we find a relation between classical topology and intuitionistic fuzzy topology. Further, we show that connectedness in intuitionistic fuzzy topological spaces are productive and we demonstrate some of its features.

scholarly journals Construction of fuzzy topology by using fuzzy metric

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 433-441
Author(s):  
Abdülkadir Aygünoğlu ◽  
Ebru Aydoğdu ◽  
Halis Aygün
Keyword(s):  
Topological Space ◽  
Fuzzy Topology ◽  
Special Interests ◽  
Fuzzy Metric ◽  
Fuzzy Topological Space

In this work, we construct a stratified fuzzy topological space induced by a fuzzy metric in the sense of Kramosil and Michalek. Our special interests are to investigate bases for such spaces and to study continuity and compactness.

scholarly journals On fuzzy generalized α-closed set and its applications

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 99-108
Author(s):  
Bayaz Daraby ◽  
S.B. Nimse
Keyword(s):  
Topological Space ◽  
Space Form ◽  
Prime Element ◽  
Fuzzy Topology ◽  
Closed Set ◽  
Closed Sets ◽  
Continuous Map ◽  
Fuzzy Topological Space

In this paper, we define and study fuzzy generalized ?-closed sets and r-open sets of a given L-fuzzy topological space and prime element r ? P(L) and coprime element a ? M(L). The concept of L-fuzzy r-open sets was introduced in [10], and it was proved that all r-open sets for L-fuzzy topological space form a new L-fuzzy topology, which is called stratiform L-fuzzy topology. Making use of the fuzzy generalized ?-closed sets, fuzzy generalized ?-continuous map is presented. .

The Spatial Dimensions of Social Networks

2020 ◽  
pp. 367-383
Author(s):  
Zachary P. Neal
Keyword(s):  
Social Networks ◽  
Topological Space ◽  
Network Science ◽  
Spatial Dimensions

The first law of geography holds that everything is related to everything else, but near things are more related than distant things, where distance refers to topographical space. If a first law of network science exists, it would similarly hold that everything is related to everything else, but near things are more related than distant things, but where distance refers to topological space. Frequently these two laws collide, together holding that everything is related to everything else, but topographically and topologically near things are more related than topographically and topologically distant things. The focus of the spatial study of social networks lies in exploring a series of questions embedded in this combined law of geography and networks. This chapter explores the questions that have been asked and the answers that have been offered at the intersection of geography and networks.

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