a set S with an associated family of subsets τ that is closed under set union and finite intersection. S and the empty set are members of τ
topological space in American English
noun
Math
a set with a collection of subsets or open sets satisfying the properties that the union of open sets is an open set, the intersection of two open sets isan open set, and the given set and the empty set are open sets
Word origin
[1945–50]This word is first recorded in the period 1945–50. Other words that entered Englishat around the same time include: RNA, individual medley, poison pill, spin-off, taxi squad
Examples of 'topological space' in a sentence
topological space
This structure characterizes an almost topological space.
Hércules A. Feitosa, Mauri C. do Nascimento, Maria Claudia C. Grácio 2010, 'Logic TK: Algebraic Notions from Tarski's Consequence Operator', Principia: An International Journal of Epistemologyhttp://www.periodicos.ufsc.br/index.php/principia/article/view/1808-1711.2010v14n1p47/17975. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Later on, the concept of soft topological space was introduced.
Taha Yasin Öztürk, Sadi Bayramov 2017, 'Topology on Soft Continuous Function Spaces', Mathematical and Computational Applicationshttp://www.mdpi.com/2297-8747/22/2/32. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We introduce the notion of generalized topological space (gt-space).
Irina Zvina 2011, 'Introduction to generalized topological spaces', Applied General Topologyhttp://polipapers.upv.es/index.php/AGT/article/view/1701. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We also investigate some operators of interval valued fuzzy neutrosophic soft topological space.
I. Arockiarani, I. R. Sumathi 2014, 'Interval Valued Fuzzy Neutrosophic Soft Structure Spaces', Neutrosophic Sets and Systemshttp://fs.gallup.unm.edu/NSS/Interval%20Valued%20Fuzzy%20Neutrosophic%20Soft.pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We continue the study of semicompact sets in a topological space.
Mohammad S. Sarsak 2009, 'On Semicompact Sets and Associated Properties', International Journal of Mathematics and Mathematical Scienceshttp://dx.doi.org/10.1155/2009/465387. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
In this paper, we shall obtain a new topology from non topological space.
Shyamapada Modak 2013, 'Operators on grill M-space', Boletim da Sociedade Paranaense de Matemáticahttp://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/15547. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Next, using the kernels of homomorphisms, we define an equivalence relation on this topological space.
Fatma Özdemir, Hasan Özekes 2013, 'On the Homomorphisms of the Lie Groups and', Abstract and Applied Analysishttp://dx.doi.org/10.1155/2013/645848. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
In this paper we introduce fuzzy weak continuity in mixed fuzzy topological space.
Binod Chandra Tripathy, Gautam Chandra Ray 2014, 'Weakly continuous functions on mixed fuzzy topological spaces', Acta Scientiarum: Technologyhttp://186.233.154.254/ojs/index.php/ActaSciTechnol/article/view/16241. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
In this paper, we introduced an algorithm to find permutation algebras using soft topological space.
Shuker Mahmood Khalil, Fatima Hameed Khadhaer 2018, 'An algorithm for generating permutation algebras using soft spaces', Journal of Taibah University for Sciencehttp://dx.doi.org/10.1080/16583655.2018.1468671. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We propose an alternative formulation of nano topological space induced by different neighbourhoods.
M. Lellis Thivagar, S.P.R. Priyalatha 2017, 'Medical diagnosis in a indiscernibility matrix based on nano topology', Cogent Mathematicshttp://dx.doi.org/10.1080/23311835.2017.1330180. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)