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Local/global uniform approximation of real-valued continuous functions

Anthony W. Hager (2011)

Commentationes Mathematicae Universitatis Carolinae

For a Tychonoff space X , C ( X ) is the lattice-ordered group ( l -group) of real-valued continuous functions on X , and C * ( X ) is the sub- l -group of bounded functions. A property that X might have is (AP) whenever G is a divisible sub- l -group of C * ( X ) , containing the constant function 1, and separating points from closed sets in X , then any function in C ( X ) can be approximated uniformly over X by functions which are locally in G . The vector lattice version of the Stone-Weierstrass Theorem is more-or-less equivalent...

Localic Katětov-Tong insertion theorem and localic Tietze extension theorem

Yong Min Li, Wang Guo-jun (1997)

Commentationes Mathematicae Universitatis Carolinae

In this paper, localic upper, respectively lower continuous chains over a locale are defined. A localic Katětov-Tong insertion theorem is given and proved in terms of a localic upper and lower continuous chain. Finally, the localic Urysohn lemma and the localic Tietze extension theorem are shown as applications of the localic insertion theorem.

Locally admissible multi-valued maps

Mirosław Ślosarski (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we generalize the class of admissible mappings as due by L. Górniewicz in 1976. Namely we define the notion of locally admissible mappings. Some properties and applications to the fixed point problem are presented.

Locally compact linearly Lindelöf spaces

Kenneth Kunen (2002)

Commentationes Mathematicae Universitatis Carolinae

There is a locally compact Hausdorff space which is linearly Lindelöf and not Lindelöf. This answers a question of Arhangel'skii and Buzyakova.

Locally compact perfectly normal spaces may all be paracompact

Paul B. Larson, Franklin D. Tall (2010)

Fundamenta Mathematicae

We work towards establishing that if it is consistent that there is a supercompact cardinal then it is consistent that every locally compact perfectly normal space is paracompact. At a crucial step we use some still unpublished results announced by Todorcevic. Modulo this and the large cardinal, this answers a question of S. Watson. Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space...

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