Small scattered topological invariants

Author V. Chatyrko, Ya. Hattori
vitja@mai.liu.se, hattori@riko.shimane-u.ac.jp
Department of Mathematics, Linkoping University, Sweden; Department of Mathematics, Shimane University, Matsue, Japan

Abstract We present a unified approach to define {dimension functions like} $\mathop{{\rm trind}}$, $\mathop{{\rm trind}}_p$, $\mathop{{\rm trt}}$ and $\mathop{{\rm p}}$. We show how some similar facts on these functions can be proved similarly. Moreover, several new classes of infinite-dimensional spaces close to the classes of countable-dimensional and $\sigma$-hereditarily disconnected ones are introduced. We prove a compactification theorem for these classes.
Keywords small transfinite inductive dimension, separation dimension, countable-dimensional spaces, $\sigma$-hereditarily disconnected spaces
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Pages 212-222
Volume 39
Issue 2
Year 2013
Journal Matematychni Studii
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