For each tile [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], we choose a planar embedding in the following way: For [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the

homeomorphism [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] must be orientation-preserving, and the vertex of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] which corresponds to [p.

Maki, semi-Generalized

Homeomorphisms and Generalized semi-Homeomorphismin topological spaces, IJPAM, 26(1995), No.

n-m] respectively, so H is a topological group

homeomorphism.

Piotrowski (1979) further investigated semi

homeomorphisms and Noiri & Ahmad (1985) introduced semi-weakly continuous functions and these functions were further characterized by Dorsett (1990).

Again by the Lebesgue dominated convergence theorem, the integral [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] because [empty set] is a

homeomorphism.

phi]] defined to be the pull-back, via a

homeomorphism [phi] : P(X) [?

c) the map [absolute value of K'] [right arrow] [absolute value of K] extending the map of vertices of K' to their corresponding points of [absolute value of K], is a

homeomorphism.

Theorem 1: Every

homeomorphism is a pre [alpha] g* closed map.

Homeomorphism is the function through which a coffee cup can be reshaped into a donut: "a function that is a one-to-one mapping between sets such that both the function and its inverse are continuous and that in topology exists for geometric figures which can be transformed one into the other by an elastic deformation" (Merriam-Webster).

Keywords and Phrases: [alpha]-finitistic space, Sum space,

Homeomorphism, Good extension property.

By first addressing the constraints of

homeomorphism, the author appeals to the approach of comparison and translation to explain the difficulty of leaving a pluralistic world for a Judeo-Christian Western world that relies on monism.

To prove the negative norm estimate for the pressure, we recall that the divergence operator is a

homeomorphism from [H.