A Study on the Concept of Connected Set

Exploring Connectedness in Topological Spaces

Authors

  • Ashwani Kumar Author

Keywords:

connected set, topological space, subset, connected space, subspace, disconnected spaces, plane, infinite line, annulus, union, disjoint closed disks, subspace topology, Euclidean space

Abstract

A subset of a topologicalspace X is a connected set if it is a connected space whenviewed as a subspace of X. An example of a spacethat is not connected is a plane with an infinite line deleted from it. Otherexamples of disconnected spaces (that is, spaces which are not connected)include the plane with an annulus removed, as well as the unionof two disjoint closed disks, where all examples of this paragraphbear the subspace topology induced bytwo-dimensional Euclidean space.

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Published

2012-08-01

Issue

Vol. 3 No. 6 (2012): Journal of Advances in Science and Technology (JAST)

Section

Articles