✦ LIBER ✦

Tri-quotient maps become inductively perfect with the aid of consonance and continuous selections

✍ Scribed by Michel Pillot

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 160 KB
Volume: 104
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(99)00018-8

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✦ Synopsis

Generalizing the result of Arhangel'skii that each open map with Čech-complete domain is compact-covering, it is proved that every tri-quotient map with consonant domain is harmonious, thus compact-covering, and its range is consonant. The latter constitutes a strong answer to a question of Nogura and Shakhmatov. Conditions for harmonious maps to be inductively perfect, or countable compact-covering and for countable compact-covering maps to be harmonious are given. They extend theorems of Just and Wicke.