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A Class of Spaces Containing all Connected and all Locally Connected Spaces

✍ Scribed by J. K. Kohli

Publisher
John Wiley and Sons
Year
1978
Tongue
English
Weight
507 KB
Volume
82
Category
Article
ISSN
0025-584X

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✦ Synopsis

A simultaneous generalization of connectedness and local connectedness, called sum connectedness, is introduced. The category of sum cohnected spaces forms the smallest co-reflective subcategory of TOP contaihing all connected spaces. A product theorem, analogous t o that for locally connected spaces, is proved for sum connected spaces and a necessary and sufficient condition for the STONE-CECH compactificetion of a TYCHONOFF space t o be sum connected is obtained. 1) See FRANKLIN [7] for the definition.

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