Continuous maps in terms of new convergence conditions
DOI:
https://doi.org/10.14419/gjma.v2i3.2986Abstract
It is well known that if X is Frechet, then a map f : X -->Y is continuous if and only if xn --> x in X implies f(xn)--> f(x) in Y . In this paper, some new convergence conditions in terms of sequences have been introduced and in terms of these convergence conditions, generalisations and analogues of some known results of continuous maps are obtained.
Keywords: Convergence, continuous, Frechet , Sequence.
References
A. Wilansky, Topology for analysis Xerox College Publishing Lexington,Massachusetts, Toronto,1970.
R. V. Fuller, Relations among continuous and various non continuous functions, Pacific J. Math. 1968. 25: 495-509.
N. Liden, K-Spaces,their anti spaces and related mappings, Pacific J.Math. 1975. 50: 505-514.
G. L. Garg, A. Goel, Convergence and perfect maps in metric spaces,Indian Journal of Pure and Applied Mathematics, 1996. 27(7):633-637.
G. L.Garg, A. Goel, Some conditions implying continuity of Maps, Acta Math. Hungarica, 1998. 81(3): 271-274.
G. L.Garg, A. Goel, Continuity of Maps in terms of cluster points,International Journal Of Pure and Applied Mathematics,2009. 51:431-435.
Downloads
Published
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal''s published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).