English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

If X is a rimhard space, then it has a realcompactification with properties similar to those of the Freudenthal compactification of a rimcompact space. 1. Rimhard spaces. All spaces discussed in this paper are assumed completely regular and Hausdorff, and all compactifications of such spaces are assumed Hausdorff. All spaces are to be nonrealcompact unless explicitly stated otherwise. Several times below, we shall be concerned with a family of extensions of a space X. In each case we shall identify two members of the family if there is a homeomorphism from one onto the other which fixes X pointwise, and we shall partially order the resulting collection of equivalence classes by aX < yX if there is a continuous map from yX onto aX which fixes X pointwise. The particular case where the family of extensions is the upper semilattice (X) of compactifications of a space X has been well studied [1i, [8], [9], [12]. K(x) has the Stone-Cech compactification 8X as its largest element and it has a smallest element, the Alexandrov compactification X*, if and only if X is locally compact. In the latter case, the lattice structure of K4(X) has been shown in [7] to characterize the topological structure of fX X. If X is a rimcompact space, i.e. has a basis of open sets with compact frontiers, then (X) contains the Freudenthal compactification FX. This is characterized [4], [10] by the properties that FX X is 0-dimensional (has a basis of open-closed sets) and if aX is any compactification such that aX X is totally disconnected, then aX < FX. Received by the editors June 12, 1973 and, in revised form, June 14, 1974. AMS (MOS) subject classifications (1970).Primary 54D05, 54D40, 54D60.

A maximal realcompactification with 0-dimensional outgrowth