Elementary Topology and Applications

Elementary topology of En

Functions of Several Variables - Undergraduate Texts in Mathematics ◽

10.1007/978-1-4684-9461-7_2 ◽

1977 ◽

pp. 28-75

Author(s):

Wendell Fleming

Keyword(s):

Elementary Topology

Elementary topology of 2 × 2 games

Topology of 2x2 Games ◽

10.4324/9780203340271-6 ◽

2004 ◽

pp. 53-76

Keyword(s):

Elementary Topology

10.1016/c2013-0-10381-9 ◽

1982 ◽

Keyword(s):

Elementary Topology

Even Covers and Collectionwise Normal Spaces

Canadian Journal of Mathematics ◽

10.4153/cjm-1978-041-6 ◽

1978 ◽

Vol 30 (03) ◽

pp. 466-473 ◽

Cited By ~ 1

Author(s):

H. L. Shapiro ◽

F. A. Smith

Keyword(s):

Sufficient Conditions ◽

Open Cover ◽

Locally Finite ◽

Finite Open Cover ◽

Elementary Topology

The concept of an even cover is introduced early in elementary topology courses and is known to be valuable. Among other facts it is known that X is paracompact if and only if every open cover of X is even. In this paper we introduce the concept of an n-even cover and show its usefulness. Using n-even we define an embedding that on closed subsets is equivalent to collectionwise normal. We also give sufficient conditions for a point finite open cover to have a locally finite refinement and also sufficient conditions for this refinement to be even. Finally we show that the collection of all neighborhoods of the diagonal of X is a uniformity if and only if every even cover is normal. This last result is particularly interesting in light of the fact that every normal open cover is even.