Abstract
AbstractGiven Hausdorff spacesXandYand a perfect irreducible and θ-continuous mapffromXontoY, technique that carries open (ultra) filters onXto open (ultra) filters onYback and forth in a natural way is introduced. It is proved that iffis a perfect irreducible and θ-continuous map fromXontoY, thenXis almost realcompact if and only ifYis almost realcompact. Several commutativity relations between the ‘absolutes of almost realcompactifications’ and the ‘almost realcompactifications of absólutes’ of a spaceXare discussed.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics,Statistics and Probability
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