Planes and Spheres as Topological Manifolds. Stereographic Projection

Marco Riccardi

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The Definition of Topological Manifolds

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This article introduces the definition of n-locally Euclidean topological spaces and topological manifolds [13].

Locally Classical Topological Benz Planes are Classical.

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Topological Manifolds

Karol Pąk (2014)

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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...

Bisectors in Minkowski 3-space.

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Continuity of Barycentric Coordinates in Euclidean Topological Spaces

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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.

The Interval [0,1] Admits no Functorial Embedding into a Finite-Dimensional or Metrizable Topological Group

Banakh, Taras, Zarichnyi, Michael (2000)

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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.

Virtual points and separating sets in spherical circle planes.

Polster, Burkard, Steinke, Günter F. (2007)

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A note on pseudobounded paratopological groups

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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...

An annulus theorem for suspension spheres

Ronald Rosen (1976)

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A note on embeddings manifolds into topological groups preserving dimensions

Hisao Kato (1992)

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