Finite and countable additivity of topological properties in nice spaces
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- by V. V. Tkachuk PDF
- Trans. Amer. Math. Soc. 341 (1994), 585-601 Request permission
Abstract:
Let $Q \in$ character $\leq \tau$, pseudocharacter $\leq \tau$, tightness $\leq \tau$, weight $\leq \tau$ , ${P_\tau }$-property, discreteness, Fréchet-Urysohn property, sequentiality, radiality, pseudoradiality, local compactness, $k$-property. If ${X^n} = \cup \{ {X_i}:i \in n\}$, ${X_i} \vdash Q$ for all $i \in n$ then $X \vdash Q$ (i.e. the property $Q$ is $n$-additive in ${X^n}$ for any $X \in {T_3}$). Metrizability is $n$-additive in ${X^n}$ provided $X$ is compact or $c(X) = \omega$. ${\text {ANR}}$-property is closely $n$-additive in ${X^n}$ if $X$ is compact ("closely" means additivity in case ${X_i}$ is closed in ${X^n}$). If $Q \in$ metrizability, character $\leq \tau$, pseudocharacter $\leq \tau$, diagonal number $\leq \tau$ , $i$-weight $\leq \tau$, pseudoweight $\leq \tau$, local compactness then $Q$ is finitely additive in any topological group.References
- P. S. Aleksandrov (ed.), Seminar po Obshcheĭ Topologii, Moskov. Gos. Univ., Moscow, 1981 (Russian). MR 656943
- M. G. Tkachenko, On a result of E. Michael and M. E. Rudin, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 5 (1981), 47–50 (Russian, with English summary). MR 635258
- E. G. Pytkeev and N. N. Yakovlev, On bicompacta which are unions of spaces defined by means of coverings, Comment. Math. Univ. Carolin. 21 (1980), no. 2, 247–261. MR 580681
- Olof Hanner, Some theorems on absolute neighborhood retracts, Ark. Mat. 1 (1951), 389–408. MR 43459, DOI 10.1007/BF02591376
- V. I. Kuz′minov, Homological dimension theory, Uspehi Mat. Nauk 23 (1968), no. 5 (143), 3–49 (Russian). MR 0240813
- A. V. Arhangel′skiĭ, On the relations between invariants of topological groups and their subspaces, Uspekhi Mat. Nauk 35 (1980), no. 3(213), 3–22 (Russian). International Topology Conference (Moscow State Univ., Moscow, 1979). MR 580615
- A. V. Arkhangel′skiĭ and D. B. Shakhmatov, Pointwise approximation of arbitrary functions by countable families of continuous functions, Trudy Sem. Petrovsk. 13 (1988), 206–227, 259 (Russian, with English summary); English transl., J. Soviet Math. 50 (1990), no. 2, 1497–1512. MR 961436, DOI 10.1007/BF01388512
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 341 (1994), 585-601
- MSC: Primary 54A25
- DOI: https://doi.org/10.1090/S0002-9947-1994-1129438-6
- MathSciNet review: 1129438