1. ONp-SPACES AND THEIR CONTINUOUS MAPS
- Author
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N V Veličko
- Subjects
Set (abstract data type) ,Discrete mathematics ,Sequence ,Pure mathematics ,General Mathematics ,Bibliography ,Mathematics::General Topology ,Order (group theory) ,Point (geometry) ,Locally compact space ,Paracompact space ,Space (mathematics) ,Mathematics - Abstract
The following theorems are the main results of this paper. Theorem 1. Let : be a closed mapping of the weakly paracompact p-space X. In order that the space Y be weakly paracompact and plumed, it is necessary and sufficient that the mapping be peripherally bicompact. Theorem 2. Let : be a closed mapping of a weakly paracompact p-space X. Then , where the set Y1 is σ-discrete in Y and the set is bicompact for each point γY0. An example is constructed of a weakly paracompact, locally compact, σ-paracompact space which is not normal and which cannot be mapped perfectly onto a space with a refining sequence of coverings. Bibliography: 22 items.
- Published
- 1973
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