The aim of this thesis is to introduce a new concept of fibrewise topological spaces which is said to be fibrewise slightly topological spaces. We generalize some of the main results that have been reached from fibrewise topology into fibrewise slightly topological space. We introduce the concepts of fibrewise slightly closed, fibrewise slightly open, fibrewise locally sliceable, and fibrewise locally sectionable slightly topological spaces. Also, state and prove several propositions related to these concepts. On the other hand, extend separation axioms of ordinary topology into fibrewise setting. The separation axioms are said to be fibrewise slightly T_0 spaces, fibrewise slightly T_1 spaces, fibrewise slightly R_0 spaces, fibrewise slightly T_2 spaces, fibrewise slightly functionally Hausdorff spaces, fibrewise slightly regular spaces, fibrewise slightly completely regular spaces, fibrewise slightly normal spaces, and fibrewise slightly functionally normal spaces have been extend. In addition, we introduce many propositions related to these concepts. Furthermore, and show the notions of fibrewise slightly compact and connected fibrewise slightly topological spaces. Finally, the concepts are studied slightly convergent, slightly directed toward in fibrewise slightly, as well fibrewise slightly perfect topological spaces, fibrewise slightly weakly closed topological spaces, fibrewise slightly almost perfect topological spaces, and fibrewise slightly* topological spaces. Also, study several theorems and characterizations concerning these concepts.
Fibrewise Slightly Topological Spaces and Their Generalizations
fibrewise slightly topological spaces
fibrewise slightly closed
fibrewise slightly open
fibrewise locally sliceable
fibrewise locally sectionable slightly topological spaces
slightly compact fibrewise slightly topological spaces
connected fibrewise slightly topological spaces.
Publication Date
Sun Feb 02 2020
Journal Name
University Of Baghdad, College Of Education For Pure Sciences / Ibn Al-haitham, Department Of Mathematics
Some Types of Perfect Mappings
j-perfect mappings
j-ω-perfect mappings
-ω-perfect mappings
weakly -ω-perfect mappings
strongly-ω-perfect mappings
nm- j-ω-converges to a subset
nm- j-ω-directed toward a set
nm- j-ω-closed mappings
nm- j-ω-rigid set
nm- j-ω-continuous mappings
nm- j-ω-perfect mappings in bitopological.
The aims of this thesis are to study the topological space; we introduce a new kind of perfect mappings, namely j-perfect mappings and j-ω-perfect mappings. Furthermore, we devoted to study the relationship between j-perfect mappings and j-ω-perfect mappings. Finally, certain theorems and characterization concerning these concepts are studied. On the other hand, we studied weakly/ strongly forms of ω-perfect mappings, namely -ω-perfect mappings, weakly -ω-perfect mappings and strongly-ω-perfect mappings; also, we investigate their fundamental properties. We devoted to study the relationship between weakly -ω-perfect mappings and strongly -ω-perfect mappings. As well as, some new generalizations of some definitions wh
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