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Author Soukup, Lajos
Source CiteSeerX
Content type Text
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Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Characterizing Continuity Preserving Compactness Connectedness ♦ Compact Subspace ♦ Elementary Theorem ♦ Continuous Function ♦ Connected Subspace ♦ Space Preserving ♦ Fre Chet ♦ Main Result ♦ Regular Space
Abstract Abstract. Let us call a function f from a space X into a space Y preserving if the image of every compact subspace of X is compact in Y and the image of every connected subspace of X is connected in Y. By elementary theorems a continuous function is always preserving. Evelyn R. McMillan [6] proved in 1970 that if X is Hausdorff, locally connected and Frèchet, Y is Hausdorff, then the converse is also true: any preserving function f: X → Y is continuous. The main result of this paper is that if X is any product of connected linearly ordered spaces (e.g. if X = Rκ) and f: X → Y is a preserving function into a regular space Y, then f is continuous. Let us call a function f from a space X into a space Y preserving if the image of every compact subspace of X is compact in Y and the image of every connected subspace of X is connected in Y. By elementary theorems a continuous function is always preserving. Quite a few authors noticed-mostly independently from each other- that the converse is also true for
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article