Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Finite and countable additivity of topological properties in nice spaces


Author: V. V. Tkachuk
Journal: Trans. Amer. Math. Soc. 341 (1994), 585-601
MSC: Primary 54A25
MathSciNet review: 1129438
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54A25

Retrieve articles in all journals with MSC: 54A25


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1129438-6
PII: S 0002-9947(1994)1129438-6
Article copyright: © Copyright 1994 American Mathematical Society