The limit space Cc(X, Y) and the connected components of X and Y

✍ Scribed by R. Vainio

• Publisher: John Wiley and Sons
• Year: 1983
• Tongue: English
• Weight: 430 KB
• Volume: 113
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19831130104

✦ Synopsis

Let X and Y be limit spaces (in the sense of FISCHER). For f E C ( X , Y), let [ f ] denote the subset of C ( X , Y), where the maps take the connected components of X into those of Y quite analogously to f. The subspace [ f ] of the continuous convergence space C,(X, Y) is written as a product 17 C,(Xi, Yk,i)), where X i runs through the components of X and Yk,i) always is the component of Y which contains the set / ( X i ) . Sufficient conditions for the representation C J X , Y)

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[ f ] are given (in terms of the spaces X and Y ) . Some applications on limit homeomorphism groups are included.