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2019•Lobachevskii Journal of MathematicsOpen access

A Note on Minimal Separating Function Sets

Raushan Z. Buzyakova, OLEG G. OKUNEV

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Abstract

We study point-separating function sets that are minimal with respect to the property of being separating. We first show that for a compact space X having a minimal separating function set in C p ( X ) is equivalent to having a minimal separating collection of functionally open sets in X . We also identify a nice visual property of X 2 that may be responsible for the existence of a minimal separating function family for X in C p ( X ). We then discuss various questions and directions around the topic.

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We study point-separating function sets that are minimal with respect to the property of being separating. We first show that for a compact space X having a minimal separating function set in C p ( X ) is equivalent to having a minimal separating collection of functionally open sets in X . We also identify a nice visual property of X 2 that may be responsible for the existence of a minimal separating function family for X in C p ( X ). We then discuss various questions and directions around the topic.

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Available abstract

We study point-separating function sets that are minimal with respect to the property of being separating. We first show that for a compact space X having a minimal separating function set in C p ( X ) is equivalent to having a minimal separating collection of functionally open sets in X . We also identify a nice visual property of X 2 that may be responsible for the existence of a minimal separating function family for X in C p ( X ). We then discuss various questions and directions around the topic.

Key concepts: Function (biology), Property (philosophy), Set (abstract data type), Point (geometry), Mathematics, Space (punctuation), Combinatorics, Minimal surface

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