Vol. 61, No. 1, 1975

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Scattered compactification for N ∪{p}

M. Jayachandran and M. Rajagopalan

Vol. 61 (1975), No. 1, 161–171
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
Authors
M. Jayachandran
M. Rajagopalan