Abstract
A convergence space is a set together with a notion of convergence of nets. It is well known how the one‐point compactification can be constructed on noncompact, locally compact topological spaces. In this paper, we discuss the construction of the one‐point compactification on noncompact convergence spaces and some of the properties of the one‐point compactification of convergence spaces are also discussed.
Highlights
A convergence space is a set together with a notion of convergence of nets
If D is directed by the relation > and m D
A convergence structure on the set X is a class C of ordered pairs such that (1) if (s,z) C, s is a net in X and x X, and (2) if (s, z) C and is a subnet of s, (t, z) C
Summary
A convergence space is a set together with a notion of convergence of nets. It is well knowr how the one-point compactification can be constructed on noncompact, locally compact topological spaces. A net is a map s whose domain is a directed set. If X is a set and s is a net with domain D, s is i__n_n X if R(s) C_X. A convergence structure on the set X is a class C of ordered pairs such that (1) if (s,z) C, s is a net in X and x X, and (2) if (s, z) C and is a subnet of s, (t, z) C.
Sign-in/Register to view highlights & summary 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 callMore From: International Journal of Mathematics and Mathematical Sciences
Disclaimer: 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.
