OPEN AND CLOSED SETS . COMPLETE METRIC SPACES
Keywords:
open set; closed set; metric space; complete metric space; f inscribed in a triangle and some special cases.Abstract
This article modern topology within open and closed sets and their metric spaces in the structure main role strict and systematic learning, especially to the fullest accent to give presented Research metric and topological in spaces open and closed sets concepts from formalization begins, their interior, closure and border operators through equivalence emphasizes. Classic to definitions based on the article associations and intersections, borders points and openness, closedness and continuity between dependency such as main features is studied. Article main direction of all Cauchy sequences approach with described complete metric spaces is the concept of. At work in analysis completeness importance, especially of borders the existence and functional of processes stability in providing is studied . Complete of spaces structural wealth show Cantor intersection for theorem and Baire category theorem such as main results discussion Statistical and bibliometric analyses this shows that functional analysis and practical in mathematics modern more than 70% of the research completeness with related to arguments relies on and this his/her theoretical and practical in the fields importance emphasizes.
References
James R. Munkres – Topology . Topology (2nd ed.). Upper Saddle River, NJ: Prentice Hall, 2000.
Walter Rudin – Mathematician analysis principles of mathematics analysis Principles (3rd ed.). New York: McGraw-Hill, 1976.
John B. Conway – Functional analysis course . Functional analysis course (2nd ed.). New York: Springer, 1990. Functional analysis in the context of complete metric spaces discussion does .
Stephen Willard – General topology . General Topology . Reading, MA: Addison-Wesley, 1970.
Topological structures advanced and strict research to do
George F. Simmons – Topology and modern to analysis Introduction . Topology and modern to analysis Introduction . New York: McGraw-Hill , 1963. Topology metric space theory and completeness with integration does .
Lynn Arthur Steen and J. Arthur Seebach – Toward Topology against examples . Topology against examples . New York: Springer, 1978.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
