A method of compactification of locally compact spaces, based on the concept of essential semilattice homomorphism, has been recently proposed. In this paper we present a natural generalization of that construction. We say that a topological space X is locally bounded with respect to a boundedness F, that is a family of subsets of X closed under finite unions and subsets, if every point of X has a bounded neighborhood. Clearly, if F is the family of relatively compact subsets of X (relatively Lindelöf subsets of a regular space X), local boundedness with respect to F is equivalent to local compactness (resp. local Lindelöfness) of X. We construct dense extensions of unbounded spaces, called B-extensions. By adding some requirements conditions, we obtain extensions that satisfy some separation and covering properties.This method can be applied, for instance, to construct Lindelöf extensions of locally Lindelöf spaces.

Extensions of unbounded topological spaces

CATERINO, Alessandro;
1998

Abstract

A method of compactification of locally compact spaces, based on the concept of essential semilattice homomorphism, has been recently proposed. In this paper we present a natural generalization of that construction. We say that a topological space X is locally bounded with respect to a boundedness F, that is a family of subsets of X closed under finite unions and subsets, if every point of X has a bounded neighborhood. Clearly, if F is the family of relatively compact subsets of X (relatively Lindelöf subsets of a regular space X), local boundedness with respect to F is equivalent to local compactness (resp. local Lindelöfness) of X. We construct dense extensions of unbounded spaces, called B-extensions. By adding some requirements conditions, we obtain extensions that satisfy some separation and covering properties.This method can be applied, for instance, to construct Lindelöf extensions of locally Lindelöf spaces.
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/11391/1032471
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact