| General topology |
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| Teaching Staff in Charge |
| Prof. NEMETH Alexandru, Ph.D., nemab@math.ubbcluj.ro |
| Aims |
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The aim of the lectures is to teach two classical results of the general topology: the imbedding of the complete regular spaces in compact Hausdorff spaces, and the imbedding of compact Hausdorff spaces of finite covering dimensions into Euclidean spaces.
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| Content |
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I. Imbedding and metrizability theorems of completely regular topological spaces. Will be revisited the notion of Tihonov product of topological spaces and will be proved Tihonov's theorem on compactity of product of topological spaces. Will be revisited the results of Urison and Tietze regarding extension of continuous functions. It will be given a detailed investigation of beses in completely regular topological spaces and will be given the method of imbedding of a such space in the Tihonov product of compact real intervals. Results regarding Stone-Cech copactification and the Uryson metrization theorem is are consequences of the developed technique.
II. Imbedding theorems of compact Hausdorff spaces in Euclidean spaces The covering dimension of a compact Hausdorff space is defined. There are given some fundamental notions and results from combinatorial and semi-linear topology. Will be defined the sceleton of a covering and will be proved the theorem of the imbedding of a compact Hausdorff space of covering dimension n into the euclidean space of dimension 2n+1. |
| References |
| Assessment |
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Exam. |