scholarly journals ON YI'S EXTENSION PROPERTY FOR TOTALLY PREORDERED TOPOLOGICAL SPACES

2006 ◽  
Vol 43 (1) ◽  
pp. 159-181 ◽  
Author(s):  
M.J. CAMPION ◽  
J.C. CANDEAL ◽  
ESTEBAN INDURAIN
Keyword(s):  
Extension Property ◽  
Topological Spaces

scholarly journals On R1 Space in l-Topological Spaces

2018 ◽  
Vol 37 ◽  
pp. 63-71
Author(s):  
Rafiqul Islam ◽  
MS Hossain
Keyword(s):  
Extension Property ◽  
Topological Spaces

In this paper, R1 space in L-topological spaces are defined and studied. We give seven definitions of R1 space in L-topological spaces and discuss certain relationship among them. We show that all of these satisfy ‘good extension’ property. Moreover, some of their other properties are obtained.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 63-71

scholarly journals Level Separation on Fuzzy Pairwise T0bitopological Space

2017 ◽  
Vol 41 (1) ◽  
pp. 57-68
Author(s):  
MS Hossain ◽  
Ummey Habiba
Keyword(s):  
Extension Property ◽  
Topological Spaces ◽  
Fuzzy Topological Spaces ◽  
Academy Of Sciences ◽  
Bitopological Spaces

In this paper, we introduce five notions of level separation in T0 fuzzy bitopological spaces. We establish some relation among them. Also, we find relations between fuzzy topological spaces and corresponding fuzzy bitopological spaces in such spaces. Further, we prove that all these definitions satisfy “good extension” property. Finally, we prove that all these notionsare hereditary, productive and projective, moreover we observe that all concepts are preserved under one-one, onto and continuous mapping.Journal of Bangladesh Academy of Sciences, Vol. 41, No. 1, 57-68, 2017

scholarly journals On R0 Space in L-Topological Spaces

2016 ◽  
Vol 40 (2) ◽  
pp. 117-124
Author(s):  
Rafiqul Islam ◽  
MS Hossain
Keyword(s):  
Extension Property ◽  
Topological Spaces ◽  
Academy Of Sciences

R0 space in L-topological spaces are defined and studied. The authors give eight definitions of R0 space in L-topological spaces and discuss certain relationship among them. They showed that all of these satisfy ‘good extension’ property. Moreover, some of their other properties are obtained.Journal of Bangladesh Academy of Sciences, Vol. 40, No. 2, 117-124, 2016

scholarly journals Fuzzy Normal Topological Space in Quasi-Coincidence Sense

2018 ◽  
Vol 42 (2) ◽  
pp. 201-205
Author(s):  
Saikh Shahj Ahan Miah ◽  
Ruhul Amin ◽  
Sohel Rana
Keyword(s):  
Topological Space ◽  
Extension Property ◽  
Topological Spaces ◽  
Continuous Mappings ◽  
Fuzzy Topological Spaces ◽  
Academy Of Sciences

Three notions of normal property in fuzzy topological spaces using quasi-coincidence sense are introduced in this paper  and relationship among these and other such notions are established. It is also shown that all these notions satisfy ‘good extension’ property. It is observed that the notions are preserved under one-one, onto, fuzzy open, fuzzy closed and fuzzy continuous mappings. Journal of Bangladesh Academy of Sciences, Vol. 42, No. 2, 201-205, 2018

scholarly journals Mappings in Fuzzy Hausdorff Spaces in Quasi-Coincidence Sense

2017 ◽  
Vol 41 (1) ◽  
pp. 47-56
Author(s):  
Saikh Shahjahan Miah ◽  
Md Ruhul Amin
Keyword(s):  
Extension Property ◽  
Topological Spaces ◽  
Hausdorff Spaces ◽  
Continuous Mappings ◽  
Fuzzy Topological Spaces ◽  
Academy Of Sciences

In this paper, we introduce two notions of T2 property in fuzzy topological spaces by using quasi-coincidence sense and we establish relationship among our and other such notions. We also show that all these notions satisfy good extension property. Also hereditary, productive and projective properties are satisfied by these notions. We observe that all these concepts are preserved under one-one, onto, fuzzy open and fuzzy continuous mappings. Finally, we discuss initial and final fuzzy topologies on our second notion.Journal of Bangladesh Academy of Sciences, Vol. 41, No. 1, 47-56, 2017

scholarly journals Homotopy Extension Property in Homotopy Theory for Topological Semigroups

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Adem Kılıçman ◽  
Amin Saif
Keyword(s):  
Homotopy Theory ◽  
Extension Property ◽  
Topological Spaces ◽  
Topological Semigroups

The purpose of this paper is to extend the concept of homotopy extension property in homotopy theory for topological spaces to its analogical structure in homotopy theory for topological semigroups. In this extension, we also give some results concerning on absolutely retract and its properties.

scholarly journals On T2 Space in L-topological Space

2015 ◽  
Vol 39 (2) ◽  
pp. 203-211
Author(s):  
Rafiqul Islam ◽  
MS Hossain ◽  
DM Ali
Keyword(s):  
Topological Space ◽  
Extension Property ◽  
Topological Spaces ◽  
Academy Of Sciences

The purpose of this paper was to construct seven concepts of T2-space in L-topological spaces. After giving the fundamental definitions, the authors established some relations among them. Further, the authors proved that all these definitions satisfy ‘good extension’ property. Finally, it is shown that these definitions are hereditary, productive and projective.Journal of Bangladesh Academy of Sciences, Vol. 39, No. 2, 203-211, 2015

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