1. For each of the statements below determine whether it is true or false, providing reasons for your answer. Let (X, T ) be a topological space and A,B ⊆ X be two compact subsets.
(a) Is A ∪ B compact ?
(b) If (X, T ) is Hausdorff, is A ∩ B compact ?
2. Let f : [a, b] → R be continuous.
(a) Prove that the map g : [a, b] → R2, x 7→ (x, f(x)) is also continuous.
(b) Prove that the graph of f is a compact subset of R2.
3. Let (X, T ) and (Y, S) be connected topological spaces. Show that X × Y is connected in the product topology.
4. Consider the subsets
X = {(x, y) : 0 ≤ x ≤ 1 , y ∈ {0, 1}} ∪ {(x, y) : 0 ≤ y ≤ 1 , x ∈ {0, 1}} and Y = X ∪ {(x, x) : 0 ≤ x ≤ 1}
of R2 with the standard topology from R2. Show that X and Y are not homeomorphic.
5. Consider the subset
Z = {(0, 0), (0, 1)} ∪ ∞, n=1 Ln
of R2 (with the standard topology from R2), where Ln = {(1/n, y) : 0 ≤ y ≤ 1} for all n ≥ 1. Let U be a non-empty subset of Z which is both open and closed in Z. Show that if U contains one of the points (0, 0) and (0, 1), then it contains the other as well.
6. Let RP2 be the real projective space as defined in lectures, and let π : S2 −→ RP2 be the natural projection. Consider R3 and R4 with the standard topologies, and let the function f : R3 −→ R4 be defined by f(x, y, z) = (x2 − z2, xy, yz, xz).
(a) Show that there exists a function g : RP2 −→ R4 such that f = g ◦ π on S2.
(b) Show that g is continuous and one-to-one.
(c) Show that g is a homeomorphism between RP2 and the subset Y = g(RP2) of R4.
In review of the art movements presented in this module including:
Impressionism, Post-Impressionism, Expressionism, Into Abstraction and the Bauhaus, Suprematism, and De Stijl; write a paragraph about the art movement that you found the most interesting.
Describe how artists used color and space in a revolutionary way period. Use your own words and references from the lectures or videos, rather than from the internet. Please use proper grammar, punctuation, and correct spelling.
Required 1 to 2 pages(attached are the lecture and the video links.
Impressionismwas a time when artists first started using color in revolutionary ways. Manet was a leader of Impressionism. In Paris, there was an Academy where artists exhibited their work called the Salon. This work created a lot of controversies when it was exhibited. It was not unusual for nude women to be painted with clothed men, the women were imaginary muses to the men. The scandalous part of this painting was that the woman was recognizable from society. Other controversial things happening in this painting include the lack of realism, and emphasis on unblended strokes and a flatness, notice the unfinished quality of the food and the lack of shading and dimension on the nude woman. In addition, the woman in the background does not quite seem to fit into the landscape.
Edouard Manet, Luncheon on the Grass (Le Déjeuner Sur L’herbe) 1863
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After Impressionism camePost-Impressionism. The way artists use color in innovative shifts further.
Seurat developed a technique that he called “divisionism.” He painted with tiny dots of color that when viewed from a distance would optically mix and we just see one color. So, tiny dots of blue and yellow would make up a field of green. Today we call this pointillism. The figures are distant and stylized. This is a fairly large painting and it took Seurat two years to paint it.
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Expressionism
Encyclopedia Britannica describes Expressionism as:
An artistic style in which the artist seeks to depict not objective reality but rather the subjective emotions and responses that objects and events arouse within a person. The artist accomplishes this aim through distortion, exaggeration, primitivism, and fantasy and through the vivid, jarring, violent, or dynamic application of formal elements.
Wikipedia describes
Munch wrote of how the painting came to be: “I was walking down the road with two friends when the sunset; suddenly, the sky turned as red as blood. I stopped and leaned against the fence, feeling unspeakably tired. Tongues of fire and blood stretched over the bluish-black fjord. My friends went on walking, while I lagged behind, shivering with fear. Then I heard the enormos, infinite scream of nature.”
He later described the personal anguish behind the painting, “for several years I was almost mad… You know my picture, ‘The Scream?’ I was stretched to the limit—nature was screaming in my blood… After that I gave up hope ever of being able to love again.”
Edvard Munch, The Shriek, 1896
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“Suprematism
was an art movement focused on basic geometric (Links to an external site.) forms, such as circles, squares, lines, and rectangles, painted in a limited range of colors. It was founded by Kazimir Malevich (Links to an external site.) in Russia…The term suprematism refers to an abstract art based upon “the supremacy of pure artistic feeling” rather than on visual depiction of objects.”
Some of the simple paintings by Malevich may be difficult to understand, it is a reduction of form to its most basic elements. Try thinking of it as a meditation, as a sort of clearing away of the subject matter or images with labels or names.
Write only at least 3 paragraph talking answer two of the the question from each chapter.
Chapter 4
Drawing on this chapter please address one of the following:
Define cultural space and discuss how cultural space is constructed through communication.
Using an example, discuss the relationship between place, power and location of enunciation?
What do we mean by hybrid cultural space? Use an example to illustrate your answer.
Chapter 5
The development of relationships across cultures can be challenging. Address the following:
a.) Describe the three stages of relationship development and discuss how intercultural issues and differences influence each stage of the relationship development process.
b.) How do inequitable relations of power with society impact intercultural relationships?
c.) Based on your understanding of intercultural communication competence, what advice would you give people who are involved in intercultural relationships? What suggestions would you give them to improve their understanding of each other and to increase the likelihood that their relationship will continue?
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