Some Characterizations of Open, Closed, and Continuous Mappings
We obtain new characterizations of open maps in terms of closures, of closed maps in terms of interiors, and of continuous maps in terms of interiors. Further open (closed) onto maps 𝑓∶𝑋→𝑌 are described in terms of images under 𝑓 of certain closed (open) sets in 𝑋. Continuity of (onto) maps is also...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/527106 |
| Summary: | We obtain new characterizations of open maps in terms of closures, of closed maps in terms of interiors, and of continuous maps in terms of interiors. Further open (closed) onto maps
𝑓∶𝑋→𝑌 are described in terms of images under 𝑓 of certain closed (open) sets in 𝑋. Continuity of (onto) maps is also characterized in terms of saturated sets. |
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| ISSN: | 0161-1712 1687-0425 |