Abstract
In this paper, the concept of weak c-structure generated by a family of functions is introduced and quotient spaces are introduced as a particular case of this. Properties of quotient maps are explored. A method of finding quotient space of topologizable and graphical c-spaces are described.
Highlights
(i, j) is 4-adjacent to (i′, j′) if |i − i′| + |j − j′| = 1 and (i, j) is 8-adjacent to (i′, j′) if max{|i − i′|, |j − j′|} = 1
In his paper [1], Reinhard Borger have the same definition for the connectivity space except that empty set is connected. Another terminology used for a c-structure is connectivity class [4,5,12] of X
Though not stated in a formal language, the smallest c-structure on a set which makes a family of functions c-continuous can be found in [1] and for a single function in [3]. We are stating it formally as weak c-structure generated by a family of functions and quotient spaces are introduced as a particular case of this
Summary
Let X be a non empty set and CX be a collection of subsets of X such that the following properties hold. A c-space X is said to be a connective space [7] if CX satisfies two more conditions as given below. In his paper [1], Reinhard Borger have the same definition for the connectivity space except that empty set is connected Another terminology used for a c-structure is connectivity class [4,5,12] of X. Elements of a c-structure are called connected sets. C is a c-structure on X and is called the strong c-structure generated by the given family of functions [11] and is denoted by. [1,7] Let B be a collection of subsets of a set X and let < B > be a c-structure on X generated by this collection(That is, the smallest c-structure on X containing B).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
