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0-dimensional 0-space Amer Auburn University Baire space balanced near collection cardinal chain chainable chunk-complex clopen closed cover closed image closed sets closed ultrafilter cluster compact metric subsets compact space compact subset contains continuum Corollary countably compact CW-complex defined denote dense equivalent exists feebly compact follows Frechet space Hausdorff space Hence hereditarily indecomposable homeomorphic homogeneous continua homogeneous plane integer inverse limit K-compact K(yX Lemma Let X,t locally compact metric locally countable locally finite map f Math mesh metric space metric-fine minimal prime open nearness space non-degenerate nonempty closed open cover open sets open subsets Pervin nearness structure prime open filter Proc Proof pseudo-arc pseudometric pX,p quasi-F RC-perfect resp result rimcompact sequence Stone-Cech compactification stratifiable spaces subspace Suppose Theorem topological space Tychonoff space ultrafilter uniform cover uniform space uniformly continuous University University Wallman compactification wfc-system zero-dimensional