Scattered compactification for N ∪{p}

M. Jayachandran and M. Rajagopalan

Vol. 61 (1975), No. 1, 161–171

DOI: 10.2140/pjm.1975.61.161

Abstract

In this paper, it is shown that the scattered space N ∪{p} admits a scattered Hausdorff compactification for a large class of points p in βN −N. This gives a partial solution to the following problem raised by Z. Semadeni in 1959: “Is there a scattered Hausdorff compactification for the space N ∪{p} where p is any point of βN − N?” (See “Sur les ensembles clairsemés,” Rozprawy Matematyczne, 19 (1959).) The proofs are purely topological and the compactifications are easy to visualize.

Mathematical Subject Classification 2000

Primary: 54D35

Secondary: 54B15

Milestones

Received: 27 November 1974

Revised: 21 July 1975

Published: 1 November 1975