On nearly Hausdorff compactifications

Sejal Shah

India

The Maharaja Sayajirao University of Baroda

Department of Mathematics, Faculty of Science

T.K. Das

India

University of Baroda

Department of Mathematics, Faculty of Science

Submitted: 2013-11-22

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Accepted: 2013-11-22

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DOI: https://doi.org/10.4995/agt.2006.1937
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Keywords:

Regular closed set, Filter, Compactification, Wallman base

Supporting agencies:

This research was not funded

Abstract:

We introduce and study here the notion of nearly Hausdorffness, a separation axiom, stronger than T1 but weaker than T2. For a space X, from a subfamily of the family of nearly Hausdorff spaces, we construct a compact nearly Hausdorff space rX containing X as a densely C*-embedded subspace. Finally, we discuss when rX is βX.

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References:

E. Cech, Topological Spaces, (John Wiley and Sons Ltd., 1966).

T. K. Das, On Projective Lift and Orbit Space, Bull. Austral. Math. Soc. 50 (1994), 445-449. http://dx.doi.org/10.1017/S0004972700013551

J. R. Porter and R. G. Woods, Extensions and Absolutes of Hausdorff Spaces, (Springer-Verlag, 1988). http://dx.doi.org/10.1007/978-1-4612-3712-9

L. A. Steen and J. A. Seebach, Jr., Counterexamples in Topology, (Springer-Verlag, 1978). http://dx.doi.org/10.1007/978-1-4612-6290-9

S. Willard, General Topology, (Addition-Wesley Pub. Comp., 1970).

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