# Some strong forms of connectedness in topological spaces

• B. K. Tyagi University of Delhi
• Sumit Singh University of Delhi
• Manoj Bhardwaj University of Delhi
• Harsh V. S. Chauhan University of Delhi

### Abstract

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.