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Connected Maps and Essentially Connected Spaces

Published online by Cambridge University Press:  20 November 2018

Eizo Nishiura*
Affiliation:
Queensborough Community College56th Avenue and Springfield Boulevard Bayside, New York11364
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Abstract

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The paper discusses some consequences of weak monotonicity for connected maps in relation to essential connectedness of a space. The first main result gives conditions under which the image by a connected map of an essentially connected space is essentially connected. The second is that, for a connected mapping of a connected, 1 .c. space to a WLOTS-wise and essentially connected space, w-monotonicity implies monotonicity. The remainder of the paper discusses continuity properties of connected, w-monotone mappings with WLOTS-wise and essentially connected range.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1985

References

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8. Pervin, W.J. and Levine, N., Connected mappings of Hausdorff spaces, Proc. Amer. Math. Soc. 9 (1958), pp. 488496.Google Scholar
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