The Definition of Topological Manifolds
Marco Riccardi (2011)
Formalized Mathematics
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This article introduces the definition of n-locally Euclidean topological spaces and topological manifolds [13].
Marco Riccardi (2011)
Formalized Mathematics
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This article introduces the definition of n-locally Euclidean topological spaces and topological manifolds [13].
Günter Steinke (1983)
Mathematische Zeitschrift
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Karol Pąk (2014)
Formalized Mathematics
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Let us recall that a topological space M is a topological manifold if M is second-countable Hausdorff and locally Euclidean, i.e. each point has a neighborhood that is homeomorphic to an open ball of E n for some n. However, if we would like to consider a topological manifold with a boundary, we have to extend this definition. Therefore, we introduce here the concept of a locally Euclidean space that covers both cases (with and without a boundary), i.e. where each point has a neighborhood...
Horváth, Á.G. (2004)
Beiträge zur Algebra und Geometrie
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Karol Pąk (2011)
Formalized Mathematics
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In this paper we present selected properties of barycentric coordinates in the Euclidean topological space. We prove the topological correspondence between a subset of an affine closed space of εn and the set of vectors created from barycentric coordinates of points of this subset.
Banakh, Taras, Zarichnyi, Michael (2000)
Serdica Mathematical Journal
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An embedding X ⊂ G of a topological space X into a topological group G is called functorial if every homeomorphism of X extends to a continuous group homomorphism of G. It is shown that the interval [0, 1] admits no functorial embedding into a finite-dimensional or metrizable topological group.
Polster, Burkard, Steinke, Günter F. (2007)
Beiträge zur Algebra und Geometrie
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Fucai Lin, Shou Lin, Iván Sánchez (2014)
Topological Algebra and its Applications
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Let G be a paratopological group. Then G is said to be pseudobounded (resp. ω-pseudobounded) if for every neighbourhood V of the identity e in G, there exists a natural number n such that G = Vn (resp.we have G = ∪ n∈N Vn). We show that every feebly compact (2-pseudocompact) pseudobounded (ω-pseudobounded) premeager paratopological group is a topological group. Also,we prove that if G is a totally ω-pseudobounded paratopological group such that G is a Lusin space, then is G a topological...
Ronald Rosen (1976)
Fundamenta Mathematicae
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Hisao Kato (1992)
Czechoslovak Mathematical Journal
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