The aim of this paper is to study the set LSK(X) of the compactifications of X which can be obtained as a supremum of singular compactifications. We prove that a compactification aX of X belongs to LSK(X) if and only if aX is the supremum of the set SC_a of the singular compactifications induced by the maps from X to a compact subspace of R which extends to aX. Then we are able to characterize the compactifications of a given space X which belong to LSK(X) and the spaces for which every compactification is the supremum of singular compactifications. Finally we prove that if SC_a generates aX then aX belongs to LSK(X) and we give some sufficient conditions in order to SC_a generate aX.

Singular compactifications and compactification lattices

CATERINO, Alessandro;VIPERA, Maria Cristina
1990

Abstract

The aim of this paper is to study the set LSK(X) of the compactifications of X which can be obtained as a supremum of singular compactifications. We prove that a compactification aX of X belongs to LSK(X) if and only if aX is the supremum of the set SC_a of the singular compactifications induced by the maps from X to a compact subspace of R which extends to aX. Then we are able to characterize the compactifications of a given space X which belong to LSK(X) and the spaces for which every compactification is the supremum of singular compactifications. Finally we prove that if SC_a generates aX then aX belongs to LSK(X) and we give some sufficient conditions in order to SC_a generate aX.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1028522
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact