Titlebook: Geometric Topology in Dimensions 2 and 3; Edwin E. Moise Textbook 1977 Springer Science+Business Media New York 1977 Cantor.Homeomorphism.

谷物

The Jordan curve theorem,The purpose of this section is to prove the following.

BIPED

Piecewise linear homeomorphisms,Let . and . be complexes. We recall, from Section 0, that a homeomorphism . is . (relative to . and .) if there is a subdivision .. of . such that for each σ ∈ .., .|σ maps σ linearly into a simplex of .. “PL” stands for piecewise linear, and “PLH” stands for PL homeomorphism, or PL homeomorphic. If .. is a subdivision of ., then we write .. < ..

vocation

PL approximations of homeomorphisms,Let [., .] and [., .’] be metric spaces, and let .: .→Y and .: .→. be mappings. Let ε be a positive number. If for each . ∈ ., .’(.(.), .(.)) < ε, then . is an ε-. of ..

针叶类的树

The triangulation theorem for 2-manifolds,In Rn, ‖P‖ denotes the norm of ., that is, the distance between . and the origin. Let

SEVER

树木中

Apogee

Isotopies,Let .. and .. be mappings .→.. A . between .. and .. is a mapping . such that .(., 0) = ..(.) and .(., 1) =..(.) for every . in .. If such a . exists, then .. and .. are ..

Noisome

Totally disconnected compact sets in ,,,The main purpose of this section is to show that every homeomorphism between two totally disconnected compact sets in .. can be extended so as to give a homeomorphism of .. onto itself.

CURB

藐视

The Antoine set,Here we present the first and classical example of wild imbedding, due to Louis Antoine [A.], [A.]. (For the definition of ., see Section 10, just after Theorem 10.4.)