Abstract:Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
“…b) card A' > 2 and there are a, 6 G A' such that a = f(b), {x G A': x G dom/, f(x) = 6} = 0 and either f(a) = a or a ^ dom/. In view of [4], 3.8, we obtain that if x E A' -{a}, then x G doing and </(.r) = f(x) and either g(a) = a or a ^ domg. It is obvious that in both cases ( 1) is valid.…”
Section: B = F*{v) = Fi-'ifiv))mentioning
confidence: 99%
“…Suppose that 1(^4,/) = I(-4,g). By virtue of [4], Theorem 3.8, (A J) and (A,g) must have the same partition into connected components. If A' is a connected component of (-4,/), then instead of f\A f or g\A' we write / and g, respectively.…”
Section: B = F*{v) = Fi-'ifiv))mentioning
confidence: 99%
“…Let us deal with the following cases: a) card A' ^ 2. Then g on A' can be defined in an arbitrary way, only A' must be a connected component of (A,g) (according to [4], 3.8). In this case also DC(A',/) = DC(A',g).…”
Section: B = F*{v) = Fi-'ifiv))mentioning
confidence: 99%
“…It is obvious that in both cases ( 1) is valid. c) (A',f) is isomorphic to some of the partial monounary algebras considered in [4], 2.1-2.7. In these sections of [4] we have described (up to isomorphism) all (A', g) with \(A', f) = 1(^4', g).…”
Section: B = F*{v) = Fi-'ifiv))mentioning
confidence: 99%
“…This paper can be considered to be a continuation of [2], [3] and [4]; in these papers analogous problems concerning the system of all convex subsets and the system of all intervals of a partial monounary algebra have been studied.…”
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
“…b) card A' > 2 and there are a, 6 G A' such that a = f(b), {x G A': x G dom/, f(x) = 6} = 0 and either f(a) = a or a ^ dom/. In view of [4], 3.8, we obtain that if x E A' -{a}, then x G doing and </(.r) = f(x) and either g(a) = a or a ^ domg. It is obvious that in both cases ( 1) is valid.…”
Section: B = F*{v) = Fi-'ifiv))mentioning
confidence: 99%
“…Suppose that 1(^4,/) = I(-4,g). By virtue of [4], Theorem 3.8, (A J) and (A,g) must have the same partition into connected components. If A' is a connected component of (-4,/), then instead of f\A f or g\A' we write / and g, respectively.…”
Section: B = F*{v) = Fi-'ifiv))mentioning
confidence: 99%
“…Let us deal with the following cases: a) card A' ^ 2. Then g on A' can be defined in an arbitrary way, only A' must be a connected component of (A,g) (according to [4], 3.8). In this case also DC(A',/) = DC(A',g).…”
Section: B = F*{v) = Fi-'ifiv))mentioning
confidence: 99%
“…It is obvious that in both cases ( 1) is valid. c) (A',f) is isomorphic to some of the partial monounary algebras considered in [4], 2.1-2.7. In these sections of [4] we have described (up to isomorphism) all (A', g) with \(A', f) = 1(^4', g).…”
Section: B = F*{v) = Fi-'ifiv))mentioning
confidence: 99%
“…This paper can be considered to be a continuation of [2], [3] and [4]; in these papers analogous problems concerning the system of all convex subsets and the system of all intervals of a partial monounary algebra have been studied.…”
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.