Open AccessSome strong forms of connectedness in topological spaces
Author(s) -
B. K. Tyagi,
Sumit Singh,
Manoj Bhardwaj,
Harsh V. S. Chauhan
Publication year - 2019
Publication title -
journal of advanced studies in topology
Language(s) - English
Resource type - Journals
eISSN - 2090-8288
pISSN - 2090-388X
DOI - 10.20454/jast.2019.1497
Subject(s) - social connectedness , mathematics , beta (programming language) , topological space , combinatorics , topology (electrical circuits) , alpha (finance) , connected component , pure mathematics , discrete mathematics , social psychology , computer science , statistics , psychology , construct validity , programming language , psychometrics
In this paper, we study new separations of sets called half separated, half \(\alpha\)-separated, half semi separated, half pre-separated, half \(\beta\)-separated sets and corresponding to these notions introduced half connected, half \(\alpha\)-connected, half semi-connected, half pre-connected, half \(\beta\)-connected topological spaces, respectively. These are stronger forms of connectedness, \(\alpha\)-connectedness, semi-connectedness, pre-connectedness, \(\beta\)-connectedness respectively. The properties of these notions follow the same pattern.