On axiomatics of transfinite dimension (in Russian)

V.A. Chatyrko

Let $\operatorname{d}$ be a dimension function and $\operatorname{trd}$ denote its transfinite extension. Axiomatics $\Sigma_{\operatorname{d}}$ and $\Sigma_{\operatorname{trd}}$ are called concordant if $\Sigma_{\operatorname{d}}$ $\subset$ $\Sigma_{\operatorname{trd}}$. Examples of concordant axiomatics are presented.

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11. K. Kuratowski, A. Mostowski Set TheoryRussian,addr Moskva– 1970

12. L.A. Luxemburg On universal infinite-dimensional spaces// Fund. Math.– 1984 V. 122 p. 129–147

	On axiomatics of transfinite dimension (in Russian)
Author	V.A. Chatyrko Dept. of Math., Lulea University, S-971 87 Lulea, Sweden
Abstract	Let $\operatorname{d}$ be a dimension function and $\operatorname{trd}$ denote its transfinite extension. Axiomatics $\Sigma_{\operatorname{d}}$ and $\Sigma_{\operatorname{trd}}$ are called concordant if $\Sigma_{\operatorname{d}}$ $\subset$ $\Sigma_{\operatorname{trd}}$. Examples of concordant axiomatics are presented.
Keywords	dimension function, transfinite extension, axiomatics, concordant axiomatics
DOI	doi:10.30970/ms.6.1.119-130
Reference	1. P.S. Aleksandrov, B.A. Pasynkov Introduction to Dimension TheoryRussian,addr Moskva – 1973 2. R. Engelking Dimension Theory, PWN,addr Warsaw– 1978 3. Yu.M. Smirnov On universal spaces for some classes of infinite-dimensional spaces Russian// Izv. Akad. Nauk SSSR V. 23– 1959 p. 185–196 4. D.W. Henderson D-dimension I. A new transfinite dimension// Pacific J. Math. V. 26– 1968 V. 26 p. 91–107 5. K. Kuratowski Topology, IIRussian,addr Moskva– 1969 6. R.H. Bing Higher-dimensional hereditarily indecomposable continua// Trans. Amer. Math. Soc.– 1951 V. 71 p. 267–273 7. V.A. Chatyrko Ordinal products of topological spaces// Fund. Math. –1994 V. 144 p. 95–117 8. R. Pol On classification of weakly infinite-dimensional compacta// Fund. Math. V. 116– 1983 p. 169–188 9. V.A. Chatyrko, B.A. Pasynkov On topological products and dimension// Vestnik MGU– 1993 V.3 10. V.A. Chatyrko Decomposing mappings and transfinite dimension// Filomat– 1993 V.7 p. 67–72 11. K. Kuratowski, A. Mostowski Set TheoryRussian,addr Moskva– 1970 12. L.A. Luxemburg On universal infinite-dimensional spaces// Fund. Math.– 1984 V. 122 p. 129–147
Pages	119-130
Volume	6
Issue	1
Year	1996
Journal	Matematychni Studii
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