Mathematics – General Topology
Scientific paper
2008-09-29
Mathematics
General Topology
21 pages
Scientific paper
A metric space X is straight if for each finite cover of X by closed sets, and for each real valued function f on X, if f is uniformly continuous on each set of the cover, then f is uniformly continuous on the whole of X. A locally connected space is straight if it is uniformly locally connected (ULC). It is easily seen that ULC spaces are stable under finite products. On the other hand the product of two straight spaces is not necessarily straight. We prove that the product X x Y of two metric spaces is straight if and only if both X and Y are straight and one of the following conditions holds: (a) both X and Y are precompact; (b) both X and Y are locally connected; (c) one of the spaces is both precompact and locally connected. In particular, when X satisfies (c), the product X x Z is straight for every straight space Z. Finally, we characterize when infinite products of metric spaces are ULC and we completely solve the problem of straightness of infinite products of ULC spaces.
Berarducci Alessandro
Dikranjan Dikran
Pelant Jan
No associations
LandOfFree
Products of straight spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Products of straight spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Products of straight spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-251788