NOTION FOR CONNECTEDNESS AND PATH CONNECTEDNESS IN SOME TYPE OF TOPOLOGICAL SPACES

  • Maja Srebrenova Miteva
  • Limonka Koceva Lazarova "Goce Delcev" UniversityFaculty of Computer Science
Keywords: connectedness; path connectedness; metric space; locally Euclidean space; Euclidean space;

Abstract

The notions of connectivity and path connectivity of topological spaces in the part of general topology are firmly related. In particular, path connectivity is a tougher condition of connectedness and reversal does not always apply. When it comes to metric space, the notion of connectedness is more difficult to formulate precisely, while the path connectedness is a concept whose definition remains the same and easier to understand in these spaces. In this text, there are examples of connectedness, path-connectedness and simultaneously connected and path-connected topological spaces. Also, an additional condition is required for which the relation of the connected space is valid to be followed by a path connected.

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Published
2018-08-07
How to Cite
Miteva, M. S., & Lazarova, L. K. (2018). NOTION FOR CONNECTEDNESS AND PATH CONNECTEDNESS IN SOME TYPE OF TOPOLOGICAL SPACES. Balkan Journal of Applied Mathematics and Informatics, 1(1), 55-62. Retrieved from https://js.ugd.edu.mk/index.php/bjami/article/view/2237
Section
Articles