Abstract
Publisher Summary This chapter introduces the recent development theory of stratifiable spaces. The chapter discusses the classes of spaces between the class of stratifiable spaces and the class of stratifiable μ -spaces. Stratifiable spaces possess nice preservation properties under various topological operations. Stratifiable μ -spaces have various dimension theoretical properties. If they are unified, then stratifiable spaces will have more validity and utility. The chapter reviews the basic results concerning stratifiable spaces. The chapter explains closure-preserving collections, definitions of various stratifiable spaces, expandability, extension property, and sup-characterization of stratifiable spaces. Closure-preserving collections give lemmas for closure-preserving collection and mosaical collections.
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