Compactness and Completeness Properties in Function Spaces

Abstract

For a Tychonoff space X, C(X) denotes the set of all real-valued continuous functions. newlineThis thesis investigates compact subsets of C(X) when C(X) is endowed with the newlinetopologies lying between the topology of pointwise convergence and the topology of newlineuniform convergence. This thesis also studies the pseudo-completeness and Baireness newlineproperties of C(X) when C(X) is endowed with the topology of uniform convergence newlineon compact subsets. This thesis introduces and studies generalized filter fans S(A, and#964; ). newlineMore precisely, we have shown that S(A, and#964; ) has the Moving Off Property (abbreviated newlineMOP) if and only if Ck(S(A, and#964; )) is Baire. newline