Preprint No. A-99-11
(Dedicated to Professor Lamar Bentley on his 60th birthday) Abstract: Higher separation axioms, paracompactness and dimension are defined for semiuniform convergence spaces. Under the assumption that subspaces are formed in the construct {\bf SUConv} of semiuniform convergence spaces one obtains the following results: $1^{0}$ Subspaces of normal (symmetric) topological spaces are normal, $2^{0}$ subspaces of paracompact topological spaces are paracompact, and $3^{0}$ for some dimension functions, the dimension of a subspace is less than or equal to the dimension of the original space, where these dimension functions coincide with the (Lebesgue) covering dimension for paracompact topological spaces. Additionally, Urysohn's Lemma, Tietze's extension theorem and some other extension theorems are studied not only in the realm of topological spaces. Last but not least the interrelations between nearness spaces and semiuniform convergence spaces become apparent.
Keywords: Complete regularity, normality, full normality, paracompactness, dimension, semiuniform convergence spaces, filter spaces, convergence spaces, topological spaces, merotopic spaces, nearness spaces, uniform spaces, maps into spheres, bireflective subcategories.
Mathematics Subject Classification (MSC91): 54A05 Topological spaces and generalizations (closure spaces, etc.) , 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
Language: ENGAvailable: Pr-A-99-11.ps
Contact: Preuß, Gerhard, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (preuss@math.fu-berlin.de)
[Home Page] - [Up] - [Search] - [Help] - Created: 19990723 -