Clanformities and h-Topological Extensions

✍ Scribed by D. Leseberg

• Publisher: John Wiley and Sons
• Year: 1991
• Tongue: English
• Weight: 471 KB
• Volume: 152
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19911520107

✦ Synopsis

Introduction. The question of when a proximity is induced by a containing topological space had been raised by RIESZ in 1908 and answered by SMIRNOV in 1952.

The analogous question concerning the more general Lodato proximities was studied by LODATO and GAGRAT and NAIMPALLY and was answered by THRON. HERRLICH investigated nearness spaces which contain the above mentioned spaces and set out to discover conditions under which a nearness space is induced by a containing topological space. BENTLEY found a solution in defining the so called bunch determined nearness spaces. A more general type of structures called ultraformities is introduced which contains also the nearness spaces and moreover the non-symmetrical LEADER proximities. Those ultraformities which can be extended to a h-topological space have a neat internal characterization in terms of suitable A-clans for each A subset of a given set X and are called clanformities.