Paracompactness of topological completions
Tadashi Ishii (1976)
Fundamenta Mathematicae
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Tadashi Ishii (1976)
Fundamenta Mathematicae
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L. G. Oversteegen, E. D. Tymchatyn (1986)
Banach Center Publications
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Kazuhiro Kawamura, Janusz Prajs (1991)
Fundamenta Mathematicae
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Witold Bula (1986)
Fundamenta Mathematicae
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K. Kawamura, E. Tymchatyn (1996)
Colloquium Mathematicae
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A symmetric, idempotent, continuous binary operation on a space is called a mean. In this paper, we provide a criterion for the non-existence of mean on a certain class of continua which includes tree-like continua. This generalizes a result of Bell and Watson. We also prove that any hereditarily indecomposable circle-like continuum admits no mean.
Teodor Przymusiński (1981)
Fundamenta Mathematicae
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Teodor Przymusiński (1976)
Fundamenta Mathematicae
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Valentin Gutev (2016)
Colloquium Mathematicae
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Strongly paracompact metrizable spaces are characterized in terms of special S-maps onto metrizable non-Archimedean spaces. A similar characterization of strongly metrizable spaces is obtained as well. The approach is based on a sieve-construction of "metric"-continuous pseudo-sections of lower semicontinuous mappings.
Zaremba, D.
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